Endpoint distribution of directed polymers in \(1 + 1\) dimensions

DOI10.1007/s00220-012-1583-zzbMath1257.82117arXiv1106.2716OpenAlexW3098417493MaRDI QIDQ1936642

Daniel Remenik, Gregorio R. Moreno Flores, Jeremy Quastel

Publication date: 6 February 2013

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

Full work available at URL: https://arxiv.org/abs/1106.2716

zbMATH Keywords

directed polymers last passage percolation nearest neighbor random walks Airy\(_{2}\) process

Mathematics Subject Classification ID

Statistical mechanics of polymers (82D60) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Time-dependent percolation in statistical mechanics (82C43)

Related Items

Airy Processes and Variational Problems ⋮ Duality between coalescence times and exit points in last-passage percolation models ⋮ Geodesic forests in last-passage percolation ⋮ Log-gamma polymer free energy fluctuations via a Fredholm determinant identity ⋮ Midpoint distribution of directed polymers in the stationary regime: exact result through linear response ⋮ The endpoint distribution of directed polymers ⋮ Local behavior and hitting probabilities of the \(\text{Airy}_1\) process ⋮ Extreme value statistics of correlated random variables: a pedagogical review ⋮ Continuum statistics of the Airy\(_{2}\) process ⋮ A Pfaffian Representation for Flat ASEP ⋮ A conditional scaling limit of the KPZ fixed point with height tending to infinity at one location ⋮ Shift-invariance of the colored TASEP and finishing times of the oriented swap process ⋮ Exceptional times when the KPZ fixed point violates Johansson's conjecture on maximizer uniqueness ⋮ Supremum of the \(\mathrm{Airy}_{2}\) process minus a parabola on a half line ⋮ Reunion probability of \(N\) vicious walkers: typical and large fluctuations for large \(N\) ⋮ Non-intersecting Brownian bridges and the Laguerre orthogonal ensemble ⋮ Non-uniqueness times for the maximizer of the KPZ fixed point ⋮ Nonintersecting Brownian motions on the half-line and discrete Gaussian orthogonal polynomials ⋮ A multi-layer extension of the stochastic heat equation ⋮ Limiting distribution of maximal crossing and nesting of Poissonized random matchings ⋮ Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence ⋮ Brownian Gibbs property for Airy line ensembles ⋮ Properties of the parabolic Anderson model and the Anderson polymer model ⋮ Power countings versus physical scalings in disordered elastic systems—case study of the one-dimensional interface ⋮ Overlaps and pathwise localization in the Anderson polymer model ⋮ One-sided reflected Brownian motions and the KPZ fixed point ⋮ Fractal geometry of \(\text{Airy}_2\) processes coupled via the Airy sheet ⋮ How flat is flat in random interface growth? ⋮ Distribution function of the endpoint fluctuations of one-dimensional directed polymers in a random potential ⋮ On global solutions of the random Hamilton–Jacobi equations and the KPZ problem ⋮ A PDE hierarchy for directed polymers in random environments ⋮ Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles ⋮ On the Location of the Maximum of a Continuous Stochastic Process ⋮ Extremes of \(N\) vicious walkers for large \(N\): application to the directed polymer and KPZ interfaces ⋮ Tails of the endpoint distribution of directed polymers ⋮ Multiplicative functionals on ensembles of non-intersecting paths ⋮ Tracy-Widom distribution, Airy\(_2\) process and its sample path properties ⋮ Localization of directed polymers in continuous space ⋮ On time correlations for KPZ growth in one dimension ⋮ A PATCHWORK QUILT SEWN FROM BROWNIAN FABRIC: REGULARITY OF POLYMER WEIGHT PROFILES IN BROWNIAN LAST PASSAGE PERCOLATION ⋮ Evolution in range expansions with competition at rough boundaries ⋮ Integration by parts and the KPZ two-point function ⋮ One-point distribution of the geodesic in directed last passage percolation

Cites Work