8,484 research outputs found
Economic development incentives: research approaches and current views
Economic development
Interacting particle systems at the edge of multilevel Dyson Brownian motions
We study the joint asymptotic behavior of spacings between particles at the
edge of multilevel Dyson Brownian motions, when the number of levels tends to
infinity. Despite the global interactions between particles in multilevel Dyson
Brownian motions, we observe a decoupling phenomenon in the limit: the global
interactions become negligible and only the local interactions remain. The
resulting limiting objects are interacting particle systems which can be
described as Brownian versions of certain totally asymmetric exclusion
processes. This is the first appearance of a particle system with local
interactions in the context of general random matrix models.Comment: 32 pages, 1 figur
Limits of Multilevel TASEP and similar processes
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.Comment: 16 pages, 1 figur
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