On ASEP with Step Bernoulli Initial Condition

Abstract

This paper extends results of earlier work on ASEP to the case of step Bernoulli initial condition. The main results are a representation in terms of a Fredholm determinant for the probability distribution of a fixed particle, and asymptotic results which in particular establish KPZ universality for this probability in one regime. (And, as a corollary, for the current fluctuations.)

16 pages. Revised version adds references and expands the introduction

References in corpus (5)

• Asymptotics in ASEP with Step Initial Condition
• A Fredholm Determinant Representation in ASEP
• Fluctuations of the one-dimensional polynuclear growth model with external sources
• A determinantal formula for the GOE Tracy-Widom distribution
• Total Current Fluctuations in ASEP

Cited by in corpus (22)

• Current Fluctuations of the Stationary ASEP and Six-Vertex Model
• Spectral theory for the q-Boson particle system
• Universality of slow decorrelation in KPZ growth
• Facilitated Asymmetric Exclusion
• Current fluctuations for TASEP: A proof of the Prähofer--Spohn conjecture
• Limit processes for TASEP with shocks and rarefaction fans
• Current moments of 1D ASEP by duality
• A Pfaffian representation for flat ASEP
• Replica approach to the KPZ equation with half Brownian motion initial condition
• Half-space stationary Kardar-Parisi-Zhang equation
• Crossover distributions at the edge of the rarefaction fan
• On integrable directed polymer models on the square lattice
• Formulas for ASEP with Two-Sided Bernoulli Initial Condition
• Distribution of a particle's position in the ASEP with the {alternating} initial condition
• The transition probability and the probability for the left-most particle's position of the q-TAZRP
• Formulas for Joint Probabilities for the Asymmetric Simple Exclusion Process
• Crossover between various initial conditions in KPZ growth: flat to stationary
• The current distribution of the multiparticle hopping asymmetric diffusion model
• Limiting current distribution for a two species asymmetric exclusion process
• Transition Probabilities of the Bethe Ansatz Solvable Interacting Particle Systems
• A Unified Interface Model for Dissipative Transport of Bosons and Fermions
• On ASEP with Periodic Step Bernoulli Initial Condition