Work

A Durrett–Remenik particle system in R d

Year: 2025

Type: article

Abstract: This paper studies a branching-selection model of motionless particles in R d , with nonlocal branching, introduced by Durrett and Remenik in dimension 1. The assumptions on the fitness function, F , and on the inhomogeneous branching distribution, are mild. The evolution equation for the macroscopic density is given by an integro-differential free boundary problem in R d , in which the free boundary represents the least F -value in the population. The main result is the characterization of the limit in probability of the empirical measure process in terms of the unique solution to this free boundary problem.

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2025.104789

Author: Rami Atar

Institution: Technion – Israel Institute of Technology

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,520

Funder: Israel Science Foundation