Formulas and Asymptotics for the Asymmetric Simple Exclusion Process

Abstract

This is an expanded version of a series of lectures delivered by the second author in June, 2009. It describes the results of three of the authors' papers on ASEP, from the derivation of exact formulas for configuration probabilities, through Fredholm determinant representation, to asymptotics for ASEP with step initial condition establishing KPZ universality. Although complete proofs are in general not given, at least the main elements of them are.

25 pages. Version 2 corrects an error in Section II.4

References in corpus (5)

• Asymptotics in ASEP with Step Initial Condition
• Integral Formulas for the Asymmetric Simple Exclusion Process
• A Fredholm Determinant Representation in ASEP
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• Formulas for Joint Probabilities for the Asymmetric Simple Exclusion Process

Cited by in corpus (6)

• Stochastic six-vertex model
• A stochastic Burgers equation from a class of microscopic interactions
• Current Fluctuations of the Stationary ASEP and Six-Vertex Model
• Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles
• Hall-Littlewood-PushTASEP and its KPZ limit
• From the totally asymmetric simple exclusion process to the KPZ fixed point