How far from the edge need a population be to survive? A probability model
Abstract
Let $N$ be a natural number. We consider a population which lives on $I_N=\{-N,-N+1,\dots,N-1,N\}$. Each individual gives birth at rate $λ$ on each of its neighboring sites and dies at rate 1. No births are allowed from the inside of $I_N$ to the outside or vice-versa. The population on the whole line (i.e. $N=+\infty$) survives with positive probability if and only if $λ>1/2$. On the other hand for any $1/2< λ\leq \sqrt 2/2$ there exists a natural number $N_c$ such that the population survives on $I_N$ for $N\geq N_c$ but dies out for $N
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Mathematical and Theoretical Epidemiology and Ecology Models
Probability and Statistical Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 February 2026
- Language
- EN
- Document type
- Preprint