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Effect of microscopic pausing time distributions on the dynamical limit shapes for random Young diagrams
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| Title: | Effect of microscopic pausing time distributions on the dynamical limit shapes for random Young diagrams |
| Authors: | Hora, Akihito Browse this author →KAKEN DB |
| Keywords: | random Young diagram | | dynamical limit shape | | pausing time distribution | | free probability | | representation of symmetric group |
| Issue Date: | 20-Aug-2020 |
| Publisher: | University of Washington |
| Journal Title: | Electronic journal of probability |
| Volume: | 25 |
| Start Page: | 70 |
| Publisher 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. |
| Rights: | https://creativecommons.org/licenses/by/4.0/ |
| Type: | article |
| URI: | http://hdl.handle.net/2115/79089 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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