Talk 6556 data/Spring

Probability Seminar (Joint UNC/DUKE)
Thursday, February 26, 2009, 4:15pm, Hanes 112, UNC Chapel Hill (AT UNC !!)
Christian Houdre
On the Limiting Shape of Random Young Tableaux for Markovian Words

In this talk, I will describe some work of Trevis Litherland and myself on limiting shape of random Young tableaux. More precisely: 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 > 3.

Generated at 7:19am Friday, April 19, 2024 by Mcal. Top * Reload * Login