A determinantal formula for the GOE Tracy-Widom distribution

Abstract

Investigating the long time asymptotics of the totally asymmetric simple exclusion process, Sasamoto obtains rather indirectly a formula for the GOE Tracy-Widom distribution. We establish that his novel formula indeed agrees with more standard expressions.

7 pages, no figures, Latex2e; To appear in J.Phys.A

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• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
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• A Pfaffian representation for flat ASEP
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• Anomalous shock fluctuations in TASEP and last passage percolation models
• One-dimensional stochastic growth and Gaussian ensembles of random matrices
• The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process
• Large fluctuations of the KPZ equation in a half-space
• Kardar-Parisi-Zhang Interfaces with Inward Growth
• Half-space stationary Kardar-Parisi-Zhang equation
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• From Painlevé to Zakharov-Shabat and beyond: Fredholm determinants and integro-differential hierarchies
• The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises
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• Fredholm determinants and pole-free solutions to the noncommutative Painleve' II equation
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• Upper tail decay of KPZ models with Brownian initial conditions
• KPZ fluctuations in finite volume
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• Hard and soft edge spacing distributions for random matrix ensembles with orthogonal and symplectic symmetry