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Exact Solution of TASEP and Generalizations

[HYBRID WORKSHOP] Integrable Structures in Random Matrix Theory and Beyond October 18, 2021 - October 22, 2021

October 18, 2021 (11:30 AM PDT - 12:20 PM PDT)
Speaker(s): Daniel Remenik (Universidad de Chile)
Location: MSRI: Simons Auditorium, Online/Virtual

  • KPZ universality class

  • biorthogonal ensemble

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC

Exact Solution Of TASEP And Generalizations


I will present a general result which allows to express the multipoint distribution of the particle locations in the totally asymmetric exclusion process (TASEP) and several related processes, for general initial conditions, in terms of the Fredholm determinant of certain kernels involving the hitting time of a random walk to a curve defined by the initial data. This scheme generalizes an earlier result for the particular case of continuous time TASEP, which has been used to prove convergence of TASEP to the KPZ fixed point. The result covers processes in continuous and discrete time, with push and block dynamics, and with sequential and parallel update, as well as some extensions to processes with memory length larger than 1. Based on joint work with Konstantin Matetski.

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Exact Solution Of TASEP And Generalizations

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