On the Limiting Shape of Markovian Random Young Tableaux
| dc.creator | Houdré, Christian | |
| dc.creator | Litherland, Trevis J. | |
| dc.date | 2008-10-16 | |
| dc.date.accessioned | 2026-07-07T10:10:43Z | |
| dc.date.available | 2026-07-07T10:10:43Z | |
| dc.description | Let $(X_n)_{n \ge 0}$ be an irreducible, aperiodic, homogeneous Markov chain, with state space an ordered finite alphabet of size $m$. Using combinatorial constructions and weak invariance principles, we obtain the limiting shape of the associated Young tableau as a multidimensional Brownian functional. Since the length of the top row of the Young tableau is also the length of the longest (weakly) increasing subsequence of $(X_k)_{1\le k \le n}$, the corresponding limiting law follows. We relate our results to a conjecture of Kuperberg by showing that, under a cyclic condition, a spectral characterization of the Markov transition matrix delineates precisely when the limiting shape is the spectrum of the traceless GUE. For $m=3$, all cyclic Markov chains have such a limiting shape, a fact previously known for $m=2$. However, this is no longer true for $m \ge 4$. | |
| dc.identifier | https://arxiv.org/abs/0810.2982 | |
| dc.identifier | http://arxiv.org/abs/0810.2982 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171673 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | 60C05; 60F05; 60F17; 60G15; 60G17; 05A16 | |
| dc.title | On the Limiting Shape of Markovian Random Young Tableaux | |
| dc.type | text |