Busemann functions and Gibbs measures in directed polymer models on \(\mathbb{Z}^2 \)

DOI10.1214/19-AOP1375zbMath1444.60083arXiv1810.03580MaRDI QIDQ2179598

Christopher Janjigian, Firas Rassoul-Agha

Publication date: 13 May 2020

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

Full work available at URL: https://arxiv.org/abs/1810.03580

zbMATH Keywords

coalescencedirected polymerscocyclerandom environmentsGibbs measuresKardar-Parisi-ZhangBusemann functionscompetition interfaceRWREDLRKPZDPREpolymer measuresviscous stochastic Burgers

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Processes in random environments (60K37)

Related Items

Dynamic polymers: invariant measures and ordering by noise ⋮ A shape theorem and a variational formula for the quenched Lyapunov exponent of random walk in a random potential ⋮ Busemann functions and semi-infinite O'Connell-Yor polymers ⋮ Busemann functions and Gibbs measures in directed polymer models on \(\mathbb{Z}^2 \) ⋮ Uniqueness and ergodicity of stationary directed polymers on \(\mathbb{Z}^2\) ⋮ The stationary horizon and semi-infinite geodesics in the directed landscape ⋮ Joint localization of directed polymers ⋮ Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique ⋮ Invariant measures for stochastic conservation laws on the line ⋮ Geometry of geodesics through Busemann measures in directed last-passage percolation ⋮ Non-existence of bi-infinite geodesics in the exponential corner growth model ⋮ Non-existence of bi-infinite polymers ⋮ Hausdorff dimensions for shared endpoints of disjoint geodesics in the directed landscape ⋮ Negative correlation of adjacent Busemann increments

Cites Work

• Uniqueness of translation-covariant zero-temperature metastate in disordered Ising ferromagnets
• Inviscid Burgers equation with random kick forcing in noncompact setting
• Busemann functions and the speed of a second class particle in the rarefaction fan
• The Burgers equation with Poisson random forcing
• Variational formulas and cocycle solutions for directed polymer and percolation models
• Bigeodesics in first-passage percolation
• Directed polymers in random environments. École d'Été de Probabilités de Saint-Flour XLVI -- 2016
• New bounds for the free energy of directed polymers in dimension \(1+1\) and \(1+2\)
• Scaling for a one-dimensional directed polymer with boundary conditions
• Stationary cocycles and Busemann functions for the corner growth model
• Geodesics and the competition interface for the corner growth model
• Fluctuation bounds for interface free energies in spin glasses
• Rounding effects of quenched randomness on first-order phase transitions
• Directed polymers in random environment are diffusive at weak disorder
• Ratios of partition functions for the log-gamma polymer
• Geodesics in first passage percolation
• Large deviations for random walk in a space-time product environment
• An improved subadditive ergodic theorem
• Density and uniqueness in percolation
• Two results concerning asymptotic behavior of solutions of the Burgers equation with force
• The Burgers equation with a random force and a general model for directed polymers in random environments
• Euclidean models of first-passage percolation
• The existence of fixed points for the \(\cdot\)/GI/1 queue.
• The attractiveness of the fixed points of a \(\cdot/\text{GI}/1\) queue.
• Invariant measures for Burgers equation with stochastic forcing
• Limiting shape for directed percolation models
• Coexistence for Richardson type competing spatial growth models
• Coexistence in two-type first-passage percolation models
• Burgers turbulence and random Lagrangian systems
• Geodesics and spanning trees for Euclidean first-passage percolation.
• Geodesics in two-dimensional first-passage percolation
• Busemann functions and equilibrium measures in last passage percolation models
• On the existence of correctors for the stochastic homogenization of viscous Hamilton-Jacobi equations
• Busemann functions and Gibbs measures in directed polymer models on \(\mathbb{Z}^2 \)
• Uniqueness and ergodicity of stationary directed polymers on \(\mathbb{Z}^2\)
• Busemann functions and infinite geodesics in two-dimensional first-passage percolation
• Quenched point-to-point free energy for random walks in random potentials
• Competition interfaces and second class particles
• Joint distribution of Busemann functions in the exactly solvable corner growth model
• Space-time stationary solutions for the Burgers equation
• A shape theorem and semi-infinite geodesics for the Hammersley model with random weights
• Localization and Perron--Frobenius theory for directed polymers
• Random Burgers equation and Lagrangian systems in non-compact domains
• Thermodynamic Limit for Directed Polymers and Stationary Solutions of the Burgers Equation
• On global solutions of the random Hamilton–Jacobi equations and the KPZ problem
• Large-Time Behavior for Viscous and Nonviscous Hamilton--Jacobi Equations Forced by Additive Noise
• Lectures on Choquet's theorem
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item