The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process

Abstract

In the totally asymmetric simple exclusion process (TASEP) two processes arise in the large time limit: the Airy_1 and Airy_2 processes. The Airy_2 process is an universal limit process occurring also in other models: in a stochastic growth model on 1+1-dimensions, 2d last passage percolation, equilibrium crystals, and in random matrix diffusion. The Airy_1 and Airy_2 processes are defined and discussed in the context of the TASEP. We also explain a geometric representation of the TASEP from which the connection to growth models and directed last passage percolation is immediate.

arXiv comment13 pages, 4 figures, proceeding for the conference in honor of Percy Deift's 60th birthday

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Cited by in corpus (14)

• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Local behavior and hitting probabilities of the Airy1 process
• Continuum statistics of the Airy2 process
• Slow decorrelations in KPZ growth
• The Airy_1 process is not the limit of the largest eigenvalue in GOE matrix diffusion
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• Tree structures for the current fluctuations in the exclusion process
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• Dimers and orthogonal polynomials: connections with random matrices
• Mapping TASEP back in time