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Mathematics > Probability

arXiv:2209.10213 (math)
[Submitted on 21 Sep 2022]

Title:Scaling limits for Rudvalis card shuffles

Authors:P. Gonçalves, M. Jara, R. Marinho, D. Moreira
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Abstract:We consider the Rudvalis card shuffle and some of its variations that were introduced by Diaconis and Saloff-Coste in \cite{symmetrized}, and we project them to some stochastic interacting particle system. For the latter, we derive the hydrodynamic limits and we study the equilibrium fluctuations. Our results show that, for these shuffles, when we consider an asymmetric variation of the Rudvalis shuffle, the hydrodynamic limit in Eulerian scale is given in terms of a transport equation with a constant that depends on the exchange rates of the system; while for symmetric and weakly asymmetric variations of this shuffle, in diffusive time scale, the evolution is given by the solution of a martingale problem.
Comments: 17 pages, 1 figure
Subjects: Probability (math.PR)
MSC classes: 82C22
Cite as: arXiv:2209.10213 [math.PR]
  (or arXiv:2209.10213v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.2209.10213

Submission history

From: Patricia Gonçalves Professor [view email]
[v1] Wed, 21 Sep 2022 09:22:42 UTC (1,151 KB)
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