The TAZRP speed process

Amir, Gideon; Busani, Ofer; Gonçalves, Patrícia; Martin, James B.

doi:10.1214/20-aihp1117

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2022

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“…The reader is referred to [AAV11] for some of the fascinacting properties of the speed process. More recent studies of speed processes appear in the papers [ACG22,ABGM21]. For our purposes, the key features of the TASEP speed process are that it itself is again invariant under suitably formulated multi-class TASEP dynamics, and it provides a simultaneous coupling of all the stationary multiclass measures µ ρ1,...,ρn for any number of particle classes.…”

Section: Introductionmentioning

confidence: 99%

Scaling limit of the TASEP speed process

Busani¹,

Seppäläinen²,

Evan³

2022

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We show that the multi-type stationary distribution of the totally asymmetric simple exclusion process (TASEP) scales to a nontrivial limit around the Bernoulli measure of density 1{2. This is obtained by showing that the TASEP speed process, introduced by Amir, Angel and Valkó, scales around the speed v " 0 to the stationary horizon (SH), a function-valued stochastic process recently introduced and studied by the authors. SH is believed to be the universal scaling limit of Busemann processes in the KPZ universality class. Our results add to the evidence for this universality by connecting SH with multiclass particle configurations. Previously SH has been associated with the exponential corner growth model, Brownian last-passage percolation, and the directed landscape.

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Section: Introductionmentioning

confidence: 99%