Midpoint distribution of directed polymers in the stationary regime: exact result through linear response

DOI10.1007/s10955-017-1839-2zbMath1374.82044arXiv1704.06909OpenAlexW3098581580MaRDI QIDQ1675340

Christian Maes, Thimothée Thiery

Publication date: 27 October 2017

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.06909

zbMATH Keywords

linear responsedirected polymerKPZ

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Brownian motion (60J65) Statistical mechanics of polymers (82D60) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Processes in random environments (60K37) PDEs in connection with statistical mechanics (35Q82)

Related Items

Another look at the Balázs-Quastel-Seppäläinen theorem ⋮ On the two-point function of the one-dimensional KPZ equation ⋮ Integration by parts and the KPZ two-point function

Cites Work

• Unnamed Item
• Unnamed Item
• Height fluctuations for the stationary KPZ equation
• Exact formulas for random growth with half-flat initial data
• Log-gamma polymer free energy fluctuations via a Fredholm determinant identity
• Stationary measures for two dual families of finite and zero temperature models of directed polymers on the square lattice
• Directed polymers in random environments. École d'Été de Probabilités de Saint-Flour XLVI -- 2016
• Random-walk in beta-distributed random environment
• Scaling for a one-dimensional directed polymer with boundary conditions
• Extremes of \(N\) vicious walkers for large \(N\): application to the directed polymer and KPZ interfaces
• Nonequilibrium linear response for Markov dynamics. I: Jump processes and overdamped diffusions
• Renormalization fixed point of the KPZ universality class
• The one-dimensional KPZ equation and its universality class
• The strict-weak lattice polymer
• Exact scaling functions for one-dimensional stationary KPZ growth
• Level-spacing distributions and the Airy kernel
• Scale invariance of the PNG droplet and the Airy process
• Limiting distributions for a polynuclear growth model with external sources
• A note on the diffusion of directed polymers in a random environment
• The asymptotics of monotone subsequences of involutions
• On orthogonal and symplectic matrix ensembles
• Endpoint distribution of directed polymers in \(1 + 1\) dimensions
• Stationary correlations for the 1D KPZ equation
• Diffusion of directed polymers in a random environment.
• Polymers on disordered trees, spin glasses, and traveling waves.
• Shape fluctuations and random matrices
• The KPZ fixed point
• Tropical combinatorics and Whittaker functions
• Macdonald processes
• The intermediate disorder regime for directed polymers in dimension \(1+1\)
• On the definition of entropy production, via examples
• On the joint distribution of the maximum and its position of the Airy2 process minus a parabola
• THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS
• Exact solution for a random walk in a time-dependent 1D random environment: the point-to-point Beta polymer
• Power countings versus physical scalings in disordered elastic systems—case study of the one-dimensional interface
• A pedestrian's view on interacting particle systems, KPZ universality and random matrices
• Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions
• The one-dimensional KPZ equation and the Airy process
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Distribution function of the endpoint fluctuations of one-dimensional directed polymers in a random potential
• Log-gamma directed polymer with fixed endpoints via the replica Bethe Ansatz
• Crossover between various initial conditions in KPZ growth: flat to stationary
• Dynamic Scaling of Growing Interfaces
• On integrable directed polymer models on the square lattice
• Airy Processes and Variational Problems
• The Kardar–Parisi–Zhang equation: a statistical physics perspective
• Current fluctuations for the totally asymmetric simple exclusion process
• Tail decay for the distribution of the endpoint of a directed polymer
• An update on the nonequilibrium linear response