Cutoff profile of the Metropolis biased card shuffling

Autor:	Zhang, Lingfu
Rok vydání:	2022
Předmět:	Mathematics - Probability Computer Science - Discrete Mathematics Mathematical Physics Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	We consider the Metropolis biased card shuffling (also called the multi-species ASEP on a finite interval or the random Metropolis scan). Its convergence to stationary was believed to exhibit a total-variation cutoff, and that was proved a few years ago by Labb\'e and Lacoin. In this paper, we prove that (for $N$ cards) the cutoff window is in the order of $N^{1/3}$, and the cutoff profile is given by the GOE Tracy-Widom distribution function. This confirms a conjecture by Bufetov and Nejjar. Our approach is different from Labb\'e-Lacoin, by comparing the card shuffling with the multi-species ASEP on $\mathbb{Z}$, and using Hecke algebra and recent ASEP shift-invariance and convergence results. Our result can also be viewed as a generalization of the Oriented Swap Process finishing time convergence of Bufetov-Gorin-Romik, which is the TASEP version (of our result). Comment: 23 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.13383 Zobrazit plný text záznamu View this record from Arxiv