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2020 Effect of microscopic pausing time distributions on the dynamical limit shapes for random Young diagrams
Akihito Hora
Electron. J. Probab. 25: 1-21 (2020). DOI: 10.1214/20-EJP466

Abstract

The irreducible decomposition of successive restriction and induction of irreducible representations of a symmetric group gives rise to a Markov chain on Young diagrams keeping the Plancherel measure invariant. Starting from this Res-Ind chain, we introduce a not necessarily Markovian continuous time random walk on Young diagrams by considering a general pausing time distribution between jumps according to the transition probability of the Res-Ind chain. We show that, under appropriate assumptions for the pausing time distribution, a diffusive scaling limit brings us concentration at a certain limit shape depending on macroscopic time which leads to a similar consequence to the exponentially distributed case studied in our earlier work. The time evolution of the limit shape is well described by using free probability theory. On the other hand, we illustrate an anomalous phenomenon observed with a pausing time obeying a one-sided stable distribution, heavy-tailed without the mean, in which a nontrivial behavior appears under a non-diffusive regime of the scaling limit.

Citation

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Akihito Hora. "Effect of microscopic pausing time distributions on the dynamical limit shapes for random Young diagrams." Electron. J. Probab. 25 1 - 21, 2020. https://doi.org/10.1214/20-EJP466

Information

Received: 12 July 2019; Accepted: 17 May 2020; Published: 2020
First available in Project Euclid: 26 June 2020

zbMATH: 1446.82068
MathSciNet: MR4119116
Digital Object Identifier: 10.1214/20-EJP466

Subjects:
Primary: 20C30, 46L54, 60J27, 82C41

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