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The purpose of this article is to describe the two approaches to compute exact formulas (which are amenable to asymptotic analysis) for the probability distribution of the current of particles past a given site in the asymmetric simple exclusion process (ASEP) with step initial data.
Zur theorie der metalle. i. eigenwerte und eigenfunktionen der linearen atomkette
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Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen q-Differenzengleichung. Das q-Analogon der Laplace-Transformation
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Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
E.H. Lieb, W. Liniger · 1963
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One-dimensional chain of anisotropic spin-spin interactions. I. Proof of Bethe’s hypothesis for the ground state in a finite system
C. N. Yang, C. P. Yang · 1966
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Convergence towards Burgers equation and propagation of chaos for weakly asymmetric exclusion process
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L. H. Gwa, H. Spohn · 1992
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Stochastic Burgers and KPZ equations from particle systems
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G. J. Heckman, E. M. Opdam · 1997
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G. M. Schütz · 1997
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T. Liggett · 2005
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A Fredholm determinant representation in ASEP
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The dynamics of the one-dimensional delta-function Bose gas
C. Tracy, H. Widom · 2008
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Asymptotics in ASEP with step initial condition
C. Tracy, H. Widom · 2009
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The crossover regime for the weakly asymmetric simple exclusion process
T. Sasamoto, H. Spohn · 2010
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Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 1+1 dimensions
G. Amir, I. Corwin, J. Quastel · 2011
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Duality relations for asymmetric exclusion processes
G. M. Schütz · 1997
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B. Sutherland · 2004
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A. Borodin, I. Corwin
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From duality to determinants for q-TASEP and ASEP
A. Borodin, I. Corwin, T. Sasamoto
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The Kardar-Parisi-Zhang equation and universality class
I. Corwin
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Current moments of 1D ASEP by duality
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Integral formulas for the asymmetric simple exclusion process
C. Tracy, H. Widom · 2011
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