Local KPZ behavior under arbitrary scaling limits

DOI10.1007/s00220-022-04492-wzbMath1498.60384arXiv2110.01062OpenAlexW3204061872MaRDI QIDQ2099803

Yanyan Li

Publication date: 18 November 2022

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.01062

zbMATH Keywords

scaling limitslocal KPZ behavior

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Statistical mechanics of polymers (82D60) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs in connection with statistical mechanics (35Q82)

Related Items (1)

Existence of stationary ballistic deposition on the infinite lattice

Cites Work

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• Weak and strong disorder for the stochastic heat equation and continuous directed polymers in \(d\geq 3\)
• KPZ line ensemble
• Solving the KPZ equation
• Log-gamma polymer free energy fluctuations via a Fredholm determinant identity
• Crossover to the KPZ equation
• A theory of regularity structures
• A stochastic Burgers equation from a class of microscopic interactions
• KPZ reloaded
• Renormalization of generalized KPZ equation
• The scaling limit of the KPZ equation in space dimension 3 and higher
• The two-dimensional KPZ equation in the entire subcritical regime
• The one-dimensional KPZ equation and its universality class
• Weakly asymmetric non-simple exclusion process and the Kardar-Parisi-Zhang equation
• Stochastic Burgers and KPZ equations from particle systems
• Scale invariance of the PNG droplet and the Airy process
• Universality in marginally relevant disordered systems
• Local behaviour of Airy processes
• Brownian aspects of the KPZ fixed point
• Brownian absolute continuity of the KPZ fixed point with arbitrary initial condition
• Edwards-Wilkinson fluctuations for the directed polymer in the full \(L^2\)-regime for dimensions \(d\ge 3\)
• Three-halves variation of geodesics in the directed landscape
• Convergence of deterministic growth models
• Law of large numbers and fluctuations in the sub-critical and \(L^2\) regions for SHE and KPZ equation in dimension \(d \geq 3\)
• Fluctuations of the solutions to the KPZ equation in dimensions three and higher
• Constructing a solution of the \((2+1)\)-dimensional KPZ equation
• Renormalizing the Kardar-Parisi-Zhang equation in \(d\ge 3\) in weak disorder
• Large scale limit of interface fluctuation models
• Fractal geometry of \(\text{Airy}_2\) processes coupled via the Airy sheet
• Gaussian fluctuations from the 2D KPZ equation
• Macdonald processes
• The intermediate disorder regime for directed polymers in dimension \(1+1\)
• Nonlinear fluctuations of weakly asymmetric interacting particle systems
• Processus linéaires, processus généralisés
• Stationary solutions to the stochastic Burgers equation on the line
• Hairer-Quastel universality in non-stationarity via energy solution theory
• Kardar-Parisi-Zhang Universality
• PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES
• Energy solutions of KPZ are unique
• Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions
• Dynamic Scaling of Growing Interfaces
• Gaussian Hilbert Spaces
• A CLASS OF GROWTH MODELS RESCALING TO KPZ
• Thermodynamic Limit for Directed Polymers and Stationary Solutions of the Burgers Equation
• Ergodicity of the KPZ Fixed Point
• Existence of stationary stochastic Burgers evolutions on R ² and R ^{3 *}
• Growth exponents of the etching model in high dimensions
• The Hairer--Quastel universality result in equilibrium
• Markov limits of steady states of the KPZ equation on an interval
• Stationary measures of the KPZ equation on an interval from Enaud–Derrida’s matrix product ansatz representation
• The crossover regime for the weakly asymmetric simple exclusion process
• Law of iterated logarithms and fractal properties of the KPZ equation
• The critical 2d stochastic heat flow
• Kardar-Parisi-Zhang equation from long-range exclusion processes
• Cutoff for the Glauber dynamics of the lattice free field

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