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A theory of regularity structures

https://doi.org/10.1007/s00222-014-0505-4

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Rough stochastic PDEs

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The partial differential equation u t + uu x = μ xx

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Orthonormal bases of compactly supported wavelets

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Positivity of the ϕ34 Hamiltonian

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A White Noise Approach to a Class of Non-linear Stochastic Heat Equations

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Two-Dimensional Navier–Stokes Equations Driven by a Space–Time White Noise

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Stochastic Partial Differential Equations

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Quantum Physics

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Differential Equations Driven by Rough Paths

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Fourier Analysis and Nonlinear Partial Differential Equations

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Continuous Martingales and Brownian Motion

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Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms

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Geometric analysis of ?4 fields and Ising models. Parts I and II

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On the stochastic quantization of field theory

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Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids

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An introduction to stochastic partial differential equations

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Scaling Limits of Wick Ordered KPZ Equation

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Taylor formula for homogenous groups and applications

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Hölder-Continuous Rough Paths by Fourier Normal Ordering

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Stochastic Burgers and KPZ Equations from Particle Systems

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Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

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Approximations to the Stochastic Burgers Equation

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Singular perturbations to semilinear stochastic heat equations

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Schauder estimates by scaling

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The Wightman axioms and the mass gap for weakly coupled (ϕ4)3 quantum field theories

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The free Markoff field

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A stochastic partial differential equation with values in a manifold

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A multiplication of distributions

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On the triviality of λϕd4 theories and the approach to the critical point in d(−) > 4 dimensions

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An extension theorem to rough paths

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A (rough) pathwise approach to a class of non-linear stochastic partial differential equations

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Ramification of rough paths

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Multidimensional Stochastic Processes as Rough Paths

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Trees, Renormalization and Differential Equations

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Lectures on Elliptic and Parabolic Equations in Sobolev Spaces

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Parabolic Anderson problem and intermittency

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On a quasi-linear parabolic equation occurring in aerodynamics

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Cocommutative Hopf algebras with antipode

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An Algebraic Theory of Integration Methods

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Deterministic and stochastic hydrodynamic equations arising from simple microscopic model systems

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System Control and Rough Paths

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Weak Solutions of a Stochastic Landau-Lifshitz-Gilbert Equation

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Dynamic Scaling of Growing Interfaces

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London Mathematical Society Monographs

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Iterated Integrals and Exponential Homomorphisms†

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A hint of renormalization

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Stochastic Navier--Stokes Equations for Turbulent Flows

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WHITE NOISE ANALYSIS

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REMARK ON THE INTEGRATION BY PARTS FORMULA FOR THE $\phi_3^4$-QUANTUM FIELD MODEL

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ANOTHER APPROACH TO SOME ROUGH AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

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Remarks on a Stochastic Quantization of Scalar Fields

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Uniqueness of solutions of the stochastic Navier–Stokes equation with invariant measure given by the enstrophy

inferredcites →https://doi.org/10.1214/07-aihp134openalex-snapshot

Homogenization of a singular random one-dimensional PDE

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Rough evolution equations

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Differential equations driven by Gaussian signals

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A spatial version of the Itô–Stratonovich correction

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Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths

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Strong solutions to the stochastic quantization equations

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Triviality of the 2D stochastic Allen-Cahn equation

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On the Structure of Hopf Algebras

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The P(φ) 2 Euclidean Quantum Field Theory as Classical Statistical Mechanics

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The Homogeneous Chaos

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An Associative Orthogonal Bilinear Form for Hopf Algebras

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Logarithmic Sobolev Inequalities

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Solving the KPZ equation

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Differential equations driven by rough signals

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Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Space‐Time Localisation for the Dynamic Model

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Directed mean curvature flow in noisy environment

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The curse of instability

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Long Term Effects of Small Random Perturbations on Dynamical Systems: Theoretical and Computational Tools

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Infinite Dimensional Rough Dynamics

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An Analyst’s Take on the BPHZ Theorem

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A Review on Comodule-Bialgebras

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Renormalization: A Quasi-shuffle Approach

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The Geometry of Characters of Hopf Algebras

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Paraproduct in Besov–Morrey Spaces

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Solving Rough Differential Equations with the Theory of Regularity Structures

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Introduction

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Random Data Wave Equations

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Construction of $$\varPhi ^4_3$$ Diagrams for Pedestrians

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Weakly Asymmetric Bridges and the KPZ Equation

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The Kardar–Parisi–Zhang Equation as Scaling Limit of Weakly Asymmetric Interacting Brownian Motions

inferred← citeshttps://doi.org/10.1007/s00220-017-2997-4openalex-snapshot

The Dynamic $${\Phi^4_3}$$ Φ 3 4 Model Comes Down from Infinity

inferred← citeshttps://doi.org/10.1007/s00220-018-3089-9openalex-snapshot

Space–Time Discrete KPZ Equation

inferred← citeshttps://doi.org/10.1007/s00220-018-3202-0openalex-snapshot

The Edwards–Wilkinson Limit of the Random Heat Equation in Dimensions Three and Higher

inferred← citeshttps://doi.org/10.1007/s00220-019-03398-4openalex-snapshot

Global Solutions to Elliptic and Parabolic $${\Phi^4}$$ Φ 4 Models in Euclidean Space

inferred← citeshttps://doi.org/10.1007/s00220-019-03527-zopenalex-snapshot

On the Moments of the $$(2+1)$$-Dimensional Directed Polymer and Stochastic Heat Equation in the Critical Window

inferred← citeshttps://doi.org/10.1007/s00220-019-03567-5openalex-snapshot

Yang–Mills Measure on the Two-Dimensional Torus as a Random Distribution

inferred← citeshttps://doi.org/10.1007/s00220-019-03665-4openalex-snapshot

A Second-Quantized Kolmogorov–Chentsov Theorem via the Operator Product Expansion

inferred← citeshttps://doi.org/10.1007/s00220-019-03678-zopenalex-snapshot

Stochastic PDE Limit of the Six Vertex Model

inferred← citeshttps://doi.org/10.1007/s00220-020-03898-8openalex-snapshot

Optimal Local Well-Posedness for the Periodic Derivative Nonlinear Schrödinger Equation

inferred← citeshttps://doi.org/10.1007/s00220-020-03905-yopenalex-snapshot

Stochastic PDE limit of the dynamic ASEP

inferred← citeshttps://doi.org/10.1007/s00220-021-04022-0openalex-snapshot

A PDE Construction of the Euclidean $$\Phi ^4_3$$ Quantum Field Theory

inferred← citeshttps://doi.org/10.1007/s00220-021-04050-wopenalex-snapshot

Short Time Large Deviations of the KPZ Equation

inferred← citeshttps://doi.org/10.1007/s00220-021-04114-xopenalex-snapshot

Stochastic Quantization of an Abelian Gauge Theory

inferred← citeshttps://doi.org/10.1007/s00220-021-04125-8openalex-snapshot

On the Parabolic and Hyperbolic Liouville Equations

inferred← citeshttps://doi.org/10.1007/s00220-021-04186-9openalex-snapshot

Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces I. The closability and quasi-regularity

inferred← citeshttps://doi.org/10.1007/s00220-022-04353-6openalex-snapshot

Phase Transitions for $$\phi ^4_3$$

inferred← citeshttps://doi.org/10.1007/s00220-022-04414-wopenalex-snapshot

Large N Limit of the O(N) Linear Sigma Model in 3D

inferred← citeshttps://doi.org/10.1007/s00220-022-04492-wopenalex-snapshot

Local KPZ Behavior Under Arbitrary Scaling Limits

inferred← citeshttps://doi.org/10.1007/s00220-022-04521-8openalex-snapshot

Conformal Field Theory from Lattice Fermions

inferred← citeshttps://doi.org/10.1007/s00220-022-04628-yopenalex-snapshot

Kardar–Parisi–Zhang Equation from Long-Range Exclusion Processes

inferred← citeshttps://doi.org/10.1007/s00220-023-04768-9openalex-snapshot

The stochastic heat equation with multiplicative L\'evy noise: Existence, moments, and intermittency

inferred← citeshttps://doi.org/10.1007/s00220-023-04885-5openalex-snapshot

The Wave Maps Equation and Brownian Paths

inferred← citeshttps://doi.org/10.1007/s00220-024-04966-zopenalex-snapshot

Gaussian Fluctuations for the Stochastic Burgers Equation in Dimension $$d\ge 2$$

inferred← citeshttps://doi.org/10.1007/s00220-024-05147-8openalex-snapshot

A Dynamical Yukawa$$_{2}$$ Model

inferred← citeshttps://doi.org/10.1007/s00220-025-05419-xopenalex-snapshot

Stochastic Quantization of the Three-Dimensional Polymer Measure via Dirichlet Form Method

inferred← citeshttps://doi.org/10.1007/s00220-025-05486-0openalex-snapshot

Hyperbolic $$P(\Phi )_2$$-model on the Plane

inferred← citeshttps://doi.org/10.1007/s00222-018-0841-xopenalex-snapshot

Algebraic renormalisation of regularity structures

inferred← citeshttps://doi.org/10.1007/s00222-020-01010-4openalex-snapshot

Classical field theory limit of many-body quantum Gibbs states in 2D and 3D

inferred← citeshttps://doi.org/10.1007/s00222-021-01084-8openalex-snapshot

Random tensors, propagation of randomness, and nonlinear dispersive equations

inferred← citeshttps://doi.org/10.1007/s00222-023-01184-7openalex-snapshot

The critical 2d Stochastic Heat Flow

inferred← citeshttps://doi.org/10.1007/s00222-023-01189-2openalex-snapshot

Full derivation of the wave kinetic equation

inferred← citeshttps://doi.org/10.1007/s00222-023-01207-3openalex-snapshot

Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift

inferred← citeshttps://doi.org/10.1007/s00222-024-01254-4openalex-snapshot

Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation

inferred← citeshttps://doi.org/10.1007/s00222-024-01264-2openalex-snapshot

Stochastic quantisation of Yang–Mills–Higgs in 3D

inferred← citeshttps://doi.org/10.1007/s00222-024-01275-zopenalex-snapshot

A diagram-free approach to the stochastic estimates in regularity structures

inferred← citeshttps://doi.org/10.1007/s00222-026-01414-8openalex-snapshot

Invariant Gibbs measures for $(1+1)$-dimensional wave maps into Lie groups

inferred← citeshttps://doi.org/10.1007/s00229-023-01510-6openalex-snapshot

On a microlocal version of Young’s product theorem

inferred← citeshttps://doi.org/10.1007/s00245-017-9459-4openalex-snapshot

Large deviations for the dynamic $\Phi^{2n}_d$ model

inferred← citeshttps://doi.org/10.1007/s00332-016-9358-xopenalex-snapshot

Metastability of the Nonlinear Wave Equation: Insights from Transition State Theory

inferred← citeshttps://doi.org/10.1007/s00332-023-09917-xopenalex-snapshot

From Second-Order Differential Geometry to Stochastic Geometric Mechanics

inferred← citeshttps://doi.org/10.1007/s00440-015-0650-8openalex-snapshot

On a modelled rough heat equation

inferred← citeshttps://doi.org/10.1007/s00440-017-0758-0openalex-snapshot

Density fluctuations for exclusion processes with long jumps

inferred← citeshttps://doi.org/10.1007/s00440-017-0781-1openalex-snapshot

Random walks and Lévy processes as rough paths

inferred← citeshttps://doi.org/10.1007/s00440-018-0841-1openalex-snapshot

Singular SPDEs in domains with boundaries

inferred← citeshttps://doi.org/10.1007/s00440-018-0849-6openalex-snapshot

Weak universality for a class of 3d stochastic reaction–diffusion models

inferred← citeshttps://doi.org/10.1007/s00440-018-0857-6openalex-snapshot

The parabolic Anderson model on Riemann surfaces

inferred← citeshttps://doi.org/10.1007/s00440-019-00920-6openalex-snapshot

Localization of the continuous Anderson Hamiltonian in 1-D

inferred← citeshttps://doi.org/10.1007/s00440-019-00926-0openalex-snapshot

Bessel SPDEs and renormalised local times

inferred← citeshttps://doi.org/10.1007/s00440-019-00938-wopenalex-snapshot

Fluctuations of the solutions to the KPZ equation in dimensions three and higher

inferred← citeshttps://doi.org/10.1007/s00440-019-00945-xopenalex-snapshot

Exponential loss of memory for the 2-dimensional Allen–Cahn equation with small noise

inferred← citeshttps://doi.org/10.1007/s00440-020-00996-5openalex-snapshot

The infinitesimal generator of the stochastic Burgers equation

inferred← citeshttps://doi.org/10.1007/s00440-022-01126-zopenalex-snapshot

Stochastic quantization associated with the $$\exp (\Phi )_2$$-quantum field model driven by space-time white noise on the torus in the full $$L^1$$-regime

inferred← citeshttps://doi.org/10.1007/s00440-022-01133-0openalex-snapshot

KPZ equation from non-simple variations on open ASEP

inferred← citeshttps://doi.org/10.1007/s00440-022-01136-xopenalex-snapshot

Grassmannian stochastic analysis and the stochastic quantization of Euclidean fermions

inferred← citeshttps://doi.org/10.1007/s00440-022-01137-wopenalex-snapshot

Singular HJB equations with applications to KPZ on the real line

inferred← citeshttps://doi.org/10.1007/s00440-022-01185-2openalex-snapshot

KPZ equation with a small noise, deep upper tail and limit shape

inferred← citeshttps://doi.org/10.1007/s00440-023-01207-7openalex-snapshot

Malliavin calculus and densities for singular stochastic partial differential equations

inferred← citeshttps://doi.org/10.1007/s00440-024-01288-yopenalex-snapshot

Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space

inferred← citeshttps://doi.org/10.1007/s00440-024-01292-2openalex-snapshot

Characterizing models in regularity structures: a quasilinear case

inferred← citeshttps://doi.org/10.1007/s00440-024-01297-xopenalex-snapshot

Effective diffusivities in periodic KPZ

inferred← citeshttps://doi.org/10.1007/s00440-024-01311-2openalex-snapshot

Martingale-driven integrals and singular SPDEs

inferred← citeshttps://doi.org/10.1007/s00440-024-01312-1openalex-snapshot

The Allen–Cahn equation with weakly critical random initial datum

inferred← citeshttps://doi.org/10.1007/s00440-024-01316-xopenalex-snapshot

The dynamical Ising-Kac model in 3D converges to $$\Phi ^4_3$$

inferred← citeshttps://doi.org/10.1007/s00440-024-01339-4openalex-snapshot

Multiplicative SHE limit of random walks in space–time random environments

inferred← citeshttps://doi.org/10.1007/s00440-024-01345-6openalex-snapshot

Localization of the continuum directed random polymer

inferred← citeshttps://doi.org/10.1007/s00440-025-01361-0openalex-snapshot

Large N limit and 1/N expansion of invariant observables in O(N) linear $$\sigma $$-model via SPDE

inferred← citeshttps://doi.org/10.1007/s00440-025-01362-zopenalex-snapshot

Jointly invariant measures for the Kardar–Parisi–Zhang equation

inferred← citeshttps://doi.org/10.1007/s00440-025-01371-yopenalex-snapshot

Rough weak solutions for singular Lévy SDEs

inferred← citeshttps://doi.org/10.1007/s00440-025-01421-5openalex-snapshot

On the multi-bubble blow-up solutions to focusing mass-critical stochastic nonlinear Schrödinger equations in dimensions one and two

inferred← citeshttps://doi.org/10.1007/s00440-026-01464-2openalex-snapshot

Towards abstract Wiener model spaces

inferred← citeshttps://doi.org/10.1007/s00440-026-01465-1openalex-snapshot

Periodic homogenisation for two dimensional generalised parabolic Anderson model

inferred← citeshttps://doi.org/10.1007/s00440-026-01515-8openalex-snapshot

Superdiffusive central limit theorem for a class of driven diffusive systems at the critical dimension

inferred← citeshttps://doi.org/10.1007/s10013-022-00570-7openalex-snapshot

Smooth Rough Paths, Their Geometry and Algebraic Renormalization

inferred← citeshttps://doi.org/10.1007/s10013-023-00672-wopenalex-snapshot

The Probabilistic Scaling Paradigm

inferred← citeshttps://doi.org/10.1007/s10114-020-9342-0openalex-snapshot

On the Small Time Asymptotics of the Dynamical Φ41 Model

inferred← citeshttps://doi.org/10.1007/s10114-020-9367-4openalex-snapshot

Convergence Rate for Galerkin Approximation of the Stochastic Allen—Cahn Equations on 2D Torus

inferred← citeshttps://doi.org/10.1007/s10208-023-09625-8openalex-snapshot

Approximations of Dispersive PDEs in the Presence of Low-Regularity Randomness

inferred← citeshttps://doi.org/10.1007/s10208-025-09701-1openalex-snapshot

Planar Regularity Structures

inferred← citeshttps://doi.org/10.1007/s10240-022-00132-0openalex-snapshot

Langevin dynamic for the 2D Yang–Mills measure

inferred← citeshttps://doi.org/10.1007/s10473-019-0304-5openalex-snapshot

On the Necessary and Sufficient Conditions to Solve A Heat Equation with General Additive Gaussian Noise

inferred← citeshttps://doi.org/10.1007/s10543-024-01046-5openalex-snapshot

Exact dimension reduction for rough differential equations

inferred← citeshttps://doi.org/10.1007/s10884-026-10498-yopenalex-snapshot

Derivation of Stochastic Burgers on the Line with a Dirichlet Boundary Condition at the Origin

inferred← citeshttps://doi.org/10.1007/s10915-023-02401-4openalex-snapshot

Feature Engineering with Regularity Structures

inferred← citeshttps://doi.org/10.1007/s10955-015-1250-9openalex-snapshot

The One-Dimensional KPZ Equation and Its Universality Class

inferred← citeshttps://doi.org/10.1007/s10955-016-1636-3openalex-snapshot

Renormalization of Generalized KPZ Equation

inferred← citeshttps://doi.org/10.1007/s10955-017-1801-3openalex-snapshot

Model Spaces of Regularity Structures for Space-Fractional SPDEs

inferred← citeshttps://doi.org/10.1007/s10955-018-2014-0openalex-snapshot

The Scaling Limit of the KPZ Equation in Space Dimension 3 and Higher

inferred← citeshttps://doi.org/10.1007/s10955-018-2200-0openalex-snapshot

Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations

inferred← citeshttps://doi.org/10.1007/s10955-019-02278-4openalex-snapshot

Local Solution to the Multi-layer KPZ Equation

inferred← citeshttps://doi.org/10.1007/s10955-019-02479-xopenalex-snapshot

Field-Theoretic Thermodynamic Uncertainty Relation

inferred← citeshttps://doi.org/10.1007/s10955-020-02539-7openalex-snapshot

Renormalizing the Kardar–Parisi–Zhang Equation in $$d\ge 3$$ in Weak Disorder

inferred← citeshttps://doi.org/10.1007/s10955-021-02866-3openalex-snapshot

The $$\Phi _3^4$$ Measure Has Sub-Gaussian Tails

inferred← citeshttps://doi.org/10.1007/s10955-023-03187-3openalex-snapshot

Properties of the Gradient Squared of the Discrete Gaussian Free Field

inferred← citeshttps://doi.org/10.1007/s10955-024-03302-yopenalex-snapshot

Derivation of Coupled KPZ Equations from Interacting Diffusions Driven by a Single-Site Potential

inferred← citeshttps://doi.org/10.1007/s10955-026-03602-5openalex-snapshot

On the Onsager-Machlup Functional of the $$\Phi ^4$$-Measure

inferred← citeshttps://doi.org/10.1007/s10959-023-01251-yopenalex-snapshot

Volterra Equations Driven by Rough Signals 3: Probabilistic Construction of the Volterra Rough Path for Fractional Brownian Motions

inferred← citeshttps://doi.org/10.1007/s11040-019-9325-5openalex-snapshot

KPZ Equation Limit of Stochastic Higher Spin Six Vertex Model

inferred← citeshttps://doi.org/10.1007/s11040-024-09488-7openalex-snapshot

A Microlocal Investigation of Stochastic Partial Differential Equations for Spinors with an Application to the Thirring Model

inferred← citeshttps://doi.org/10.1007/s11040-025-09515-1openalex-snapshot

The Ising model: highlights and perspectives

inferred← citeshttps://doi.org/10.1007/s11118-020-09830-yopenalex-snapshot

An Itô Formula for rough partial differential equations and some applications

inferred← citeshttps://doi.org/10.1007/s11118-021-09941-0openalex-snapshot

Weak Universality of the Dynamical ${{\Phi }_{3}^{4}}$ Model on the Whole Space

inferred← citeshttps://doi.org/10.1007/s11118-021-09976-3openalex-snapshot

Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise

inferred← citeshttps://doi.org/10.1007/s11118-022-10018-9openalex-snapshot

Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces

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