THE MORAN MODEL WITH RANDOM RESAMPLING RATES
成果类型：
Article
署名作者：
Athreya, Siva; Den Hollander, Frank; Rollin, Adrian
署名单位：
Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru; Leiden University - Excl LUMC; Leiden University; National University of Singapore
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/25-AAP2159
发表日期：
2025
页码：
1852-1868
关键词：
摘要：
In this paper we consider the two-type Moran model with N individuals. Each individual is assigned a resampling rate, drawn independently from a probability distribution P on R+, and a type, either 1 or 0. Each individual resamples its type at its assigned rate, by adopting the type of an individual drawn uniformly at random. Let Y-N (t) denote the empirical distribution of the resampling rates of the individuals with type 1 at time Nt. We show that if P has countable support and satisfies certain tail and moment conditions, then in the limit as N -> infinity the process (Y-N (t))(t >= 0) converges in law to the process (S(t)P)(t>0), in the so-called Meyer-Zheng topology, where (S(t))(t >= 0) is the Fisher-Wright diffusion with diffusion constant D given by 1/D = f(R+)(1/r)P(dr).