Universality in marginally relevant disordered systems

DOI10.1214/17-AAP1276zbMath1387.82032arXiv1510.06287OpenAlexW2222840913MaRDI QIDQ1688026

Nikos Zygouras, Rongfeng Sun, Francesco Caravenna

Publication date: 4 January 2018

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.06287

zbMATH Keywords

stochastic heat equationpolynomial chaosfourth-moment theoremdisordered systemdirected polymerpinning modelmarginal disorder relevance

Mathematics Subject Classification ID

Related Items (52)

The near-critical Gibbs measure of the branching random walk ⋮ A forward-backward SDE from the 2D nonlinear stochastic heat equation ⋮ Positive random walks and an identity for half-space SPDEs ⋮ Rescaled Whittaker driven stochastic differential equations converge to the additive stochastic heat equation ⋮ Gaussian limits for subcritical chaos ⋮ Law of large numbers and fluctuations in the sub-critical and \(L^2\) regions for SHE and KPZ equation in dimension \(d \geq 3\) ⋮ Central limit theorem for Gibbs measures on path spaces including long range and singular interactions and homogenization of the stochastic heat equation ⋮ Fluctuations of the solutions to the KPZ equation in dimensions three and higher ⋮ Constructing a solution of the \((2+1)\)-dimensional KPZ equation ⋮ Moments of the 2D SHE at criticality ⋮ Moments of partition functions of 2d Gaussian polymers in the weak disorder regime-I ⋮ Total variation distance between stochastic polynomials and invariance principles ⋮ Fluctuations of two-dimensional stochastic heat equation and KPZ equation in subcritical regime for general initial conditions ⋮ Weak convergence of directed polymers to deterministic KPZ at high temperature ⋮ The critical 2d stochastic heat flow ⋮ Universality: random matrices, random geometry and SPDEs. Abstracts from the workshop held May 29 -- June 4, 2022 ⋮ Delta-Bose gas from the viewpoint of the two-dimensional stochastic heat equation ⋮ Large scale stochastic dynamics. Abstracts from the workshop held September 11--17, 2022 ⋮ Mesoscopic averaging of the two-dimensional KPZ equation ⋮ Central limit theorems for the \((2 + 1)\)-dimensional directed polymer in the weak disorder limit ⋮ Moments of the 2D directed polymer in the subcritical regime and a generalisation of the Erdös-Taylor theorem ⋮ The critical 2d stochastic heat flow is not a Gaussian multiplicative chaos ⋮ Weak-disorder limit for directed polymers on critical hierarchical graphs with vertex disorder ⋮ PINNING ON A DEFECT LINE: CHARACTERIZATION OF MARGINAL DISORDER RELEVANCE AND SHARP ASYMPTOTICS FOR THE CRITICAL POINT SHIFT ⋮ Some recent progress in singular stochastic partial differential equations ⋮ Fluctuations of a Nonlinear Stochastic Heat Equation in Dimensions Three and Higher ⋮ Existence of stationary stochastic Burgers evolutions on R ² and R ^{3 *} ⋮ 2D anisotropic KPZ at stationarity: scaling, tightness and nontriviality ⋮ The Edwards-Wilkinson limit of the random heat equation in dimensions three and higher ⋮ Localization of directed polymers with general reference walk ⋮ A bound on the Wasserstein-2 distance between linear combinations of independent random variables ⋮ On the moments of the \((2+1)\)-dimensional directed polymer and stochastic heat equation in the critical window ⋮ The Dickman subordinator, renewal theorems, and disordered systems ⋮ Another look into the Wong-zakai theorem for stochastic heat equation ⋮ Stochastic PDEs on graphs as scaling limits of discrete interacting systems ⋮ Gaussian fluctuations for the directed polymer partition function in dimension \(d\ge 3\) and in the whole \(L^2\)-region ⋮ Weak-disorder limit at criticality for directed polymers on hierarchical graphs ⋮ The scaling limit of the directed polymer with power-law tail disorder ⋮ Localization of the Gaussian multiplicative chaos in the Wiener space and the stochastic heat equation in strong disorder ⋮ Continuum directed random polymers on disordered hierarchical diamond lattices ⋮ Gaussian fluctuations from the 2D KPZ equation ⋮ The random heat equation in dimensions three and higher: the homogenization viewpoint ⋮ Scaling limit of a directed polymer among a Poisson field of independent walks ⋮ High-temperature scaling limit for directed polymers on a hierarchical lattice with bond disorder ⋮ The continuum directed polymer in Lévy noise ⋮ The intermediate disorder regime for Brownian directed polymers in Poisson environment ⋮ Edwards-Wilkinson fluctuations for the directed polymer in the full \(L^2\)-regime for dimensions \(d\ge 3\) ⋮ The two-dimensional KPZ equation in the entire subcritical regime ⋮ The multivariate functional de Jong CLT ⋮ Local KPZ behavior under arbitrary scaling limits ⋮ Continuum models of directed polymers on disordered diamond fractals in the critical case ⋮ Weak coupling limits for directed polymers in tube environments

This page was built for publication: Universality in marginally relevant disordered systems