2022/03/16 by Joseph S. Alameda, Caroline Bang, Alameda, Joseph S. +9
Computer Science · Mathematics · #37A25 #60J10 #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2203.08647
openalex publication_date 2022/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers the (n,k)-Bernoulli--Laplace model in the case when there are two urns, the total number of red and white balls is the same, and the number of selections k at each step is on the same asymptotic order as the number of balls n in each urn. Our main focus is on the large-time behavior of the corresponding Markov chain tracking the number of red balls in a given urn. Under reasonable assumptions on the asymptotic behavior of the ratio k/n as n→ ∞, cutoff in the total variation distance is established. A cutoff window is also provided. These results, in particular, partially resolve an open problem posed by Eskenazis and Nestoridi.