학술논문
Cutoff in the Bernoulli-Laplace urn model with swaps of order $n$.
Document Type
Journal
Author
Alameda, Joseph S. (1-USNA-NDM) AMS Author Profile; Bang, Caroline (1-IASU-NDM) AMS Author Profile; Brennan, Zachary (1-IASU-NDM) AMS Author Profile; Herzog, David P. (1-IASU-NDM) AMS Author Profile; Kritschgau, Jürgen (1-CMU-NDM) AMS Author Profile; Sprangel, Elizabeth (1-IASU-NDM) AMS Author Profile
Source
Subject
37 Dynamical systems and ergodic theory -- 37A Ergodic theory
37A25Ergodicity, mixing, rates of mixing
37A25
Language
English
Abstract
Summary: ``This paper considers the $(n, k)$-Bernoulli-Laplace urn model in the case when there are two urns containing $n$ balls each, with two different colors of balls (red and white). In our setting, the total number of red and white balls is the same. Our focus is on the large-time behavior of the corresponding Markov chain tracking the number of red balls in a given urn assuming that the number of selections $k$ at each step obeys $\alpha \leq k/n \leq \beta$, where $\alpha$, $\beta$ are constants satisfying $0 < \alpha < \beta < \frac 12$. Under this assumption, cutoff in the total variation distance is established and a cutoff window is provided. The results in this paper solve an open problem posed by Eskenazis and Nestoridi in [8] [MR4164850].''