Directed polymers in a random environment: a review of the phase transitions

DOI10.1016/J.SPA.2024.104431MaRDI QIDQ6615507

Nikos Zygouras

Publication date: 8 October 2024

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

martingalesphase transitionsdisordered systemshierarchical latticescoarse grainingfractional moment methodpinning modelsrandom polymersheavy tail disorderintermediate disorder regimeweak and strong disorder

Mathematics Subject Classification ID

Statistical mechanics of polymers (82D60) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Phase transitions (general) in equilibrium statistical mechanics (82B26) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Critical phenomena in equilibrium statistical mechanics (82B27) Processes in random environments (60K37) Random measures (60G57) Fractional partial differential equations (35R11)

Cites Work

• Fractional moment bounds and disorder relevance for pinning models
• The directed landscape
• Correction to: ``Quenched large deviation principle for words in a letter sequence
• The stochastic heat equation with multiplicative Lévy noise: existence, moments, and intermittency
• The conditional Gaussian multiplicative chaos structure underlying a critical continuum random polymer model on a diamond fractal
• Moment characterization of the weak disorder phase for directed polymers in a class of unbounded environments
• The critical 2d stochastic heat flow is not a Gaussian multiplicative chaos
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• KPZ line ensemble
• Localization in log-gamma polymers with boundaries
• Solving the KPZ equation
• Log-gamma polymer free energy fluctuations via a Fredholm determinant identity
• Directed polymers and the quantum Toda lattice
• Gaussian multiplicative chaos and applications: a review
• High temperature limits for \((1+1)\)-dimensional directed polymer with heavy-tailed disorder
• Polynomial chaos and scaling limits of disordered systems
• Directed polymers in random environments. École d'Été de Probabilités de Saint-Flour XLVI -- 2016
• The high-temperature behavior for the directed polymer in dimension \(1+2\)
• Disorder and critical phenomena through basic probability models. École d'Été de Probabilités de Saint-Flour XL -- 2010.
• New bounds for the free energy of directed polymers in dimension \(1+1\) and \(1+2\)
• Disorder relevance for the random walk pinning model in dimension 3
• On the critical point of the random walk pinning model in dimension \(d=3\)
• Scaling for a one-dimensional directed polymer with boundary conditions
• Quenched large deviation principle for words in a letter sequence
• Geometric RSK correspondence, Whittaker functions and symmetrized random polymers
• The two-dimensional KPZ equation in the entire subcritical regime
• Directed polymers in random environment are diffusive at weak disorder
• Heavy tails in last-passage percolation
• Strong localization and macroscopic atoms for directed polymers
• The one-dimensional KPZ equation and its universality class
• A central limit theorem for generalized multilinear forms
• Disordered pinning models and copolymers: Beyond annealed bounds
• Directed polymers on hierarchical lattices with site disorder
• Noise stability of functions with low influences: invariance and optimality
• Annealed vs quenched critical points for a random walk pinning model
• Random polymers.
• Extremes and related properties of random sequences and processes
• A central limit theorem for generalized quadratic forms
• KPP equation and supercritical branching Brownian motion in the subcritical speed area. Application to spatial trees
• A remark on diffusion of directed polymers in random environments
• Improved bounds for the transition temperature of directed polymers in a finite-dimensional random medium
• Scale invariance of the PNG droplet and the Airy process
• Discrete polynuclear growth and determinantal processes
• Directed polymers in a random environment: Path localization and strong disorder
• The stochastic heat equation: Feynman-Kac formula and intermittence.
• Universality in marginally relevant disordered systems
• Nested critical points for a directed polymer on a disordered diamond lattice
• Brownian analogues of Burke's theorem.
• A condition for weak disorder for directed polymers in random environment
• A note on the diffusion of directed polymers in a random environment
• On the partition function of a directed polymer in a Gaussian random environment
• A martingale approach to directed polymers in a random environment
• Diffusion of directed polymers in a random environment.
• Polymers on disordered trees, spin glasses, and traveling waves.
• Shape fluctuations and random matrices
• Directed polymer in \(\gamma\)-stable random environments
• Directed polymers on infinite graphs
• Full-path localization of directed polymers
• Weak-disorder limit at criticality for directed polymers on hierarchical graphs
• The KPZ fixed point
• New characterization of the weak disorder phase of directed polymers in bounded random environments
• The continuum directed polymer in Lévy noise
• Edwards-Wilkinson fluctuations for the directed polymer in the full \(L^2\)-regime for dimensions \(d\ge 3\)
• Continuum models of directed polymers on disordered diamond fractals in the critical case
• A forward-backward SDE from the 2D nonlinear 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 \(d \geq 3\)
• The endpoint distribution of directed polymers
• Marginal relevance for the \(\gamma \)-stable pinning model
• Renormalizing the Kardar-Parisi-Zhang equation in \(d\ge 3\) in weak disorder
• Localization in Gaussian disordered systems at low temperature
• The Dickman subordinator, renewal theorems, and disordered systems
• Continuum directed random polymers on disordered hierarchical diamond lattices
• Hierarchical pinning models, quadratic maps and quenched disorder
• The intermediate disorder regime for a directed polymer model on a hierarchical lattice
• Entropy-controlled last-passage percolation
• Free energy of directed polymers in random environment in \(1+1\)-dimension at high temperature
• Brownian Gibbs property for Airy line ensembles
• Integrable probability: from representation theory to MacDonald processes
• Tropical combinatorics and Whittaker functions
• The intermediate disorder regime for directed polymers in dimension \(1+1\)
• Nonlinear fluctuations of weakly asymmetric interacting particle systems
• Central limit theorems for sequences of multiple stochastic integrals
• Moments of the 2D SHE at criticality
• Some algebraic structures in KPZ universality
• Two-point convergence of the stochastic six-vertex model to the Airy process
• THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS
• PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES
• Directed polymers in a random environment with heavy tails
• Energy solutions of KPZ are unique
• Dynamic Scaling of Growing Interfaces
• Percolation
• On the distribution of the length of the longest increasing subsequence of random permutations
• Gaussian Hilbert Spaces
• Probability
• A CLASS OF GROWTH MODELS RESCALING TO KPZ
• Variants of Geometric RSK, Geometric PNG, and the Multipoint Distribution of the Log-Gamma Polymer
• Lectures on integrable probability
• A remark concerning random walks with random potentials
• The two-dimensional stochastic heat equation: renormalizing a multiplicative noise
• Convergence of exclusion processes and the KPZ equation to the KPZ fixed point
• Extreme value problems in random matrix theory and other disordered systems
• Lectures on random polymers
• Combinatorics and Random Matrix Theory

This page was built for publication: Directed polymers in a random environment: a review of the phase transitions

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6615507)