Limits of Multilevel TASEP and similar processes

Abstract

We study the asymptotic behavior of a class of stochastic dynamics on interlacing particle configurations (also known as Gelfand-Tsetlin patterns). Examples of such dynamics include, in particular, a multi-layer extension of TASEP and particle dynamics related to the shuffling algorithm for domino tilings of the Aztec diamond. We prove that the process of reflected interlacing Brownian motions introduced by Warren in \cite{W} serves as a universal scaling limit for such dynamics.

16 pages, 1 figure

References in corpus (2)

• Elliptically Distributed Lozenge Tilings of a Hexagon
• On the Shuffling Algorithm for Domino Tilings

Cited by in corpus (8)

• Macdonald processes, quantum integrable systems and the Kardar-Parisi-Zhang universality class
• One-sided reflected Brownian motions and the KPZ fixed point
• Interlacing Diffusions
• Finite GUE distribution with cut-off at a shock
• Multilevel Dyson Brownian motions via Jack polynomials
• Laguerre and Jacobi analogues of the Warren process
• Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity
• Parameter symmetry in perturbed GUE corners process and reflected drifted Brownian motions