Limits of Multilevel TASEP and similar processes

Understand

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.