On the balance between Emigration and Immigration as Random Walks on the non-negative integers

2023/04/17 by Thierry Huillet, Huillet, Thierry
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Biological sciences #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Physics and Society (physics.soc-ph) #Populations and Evolution (q-bio.PE) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2304.08060

openalex publication_date 2023/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Life is on the razor's edge as resulting from competitive birth and death random forces. We illustrate this aphorism in the context of three Markov chain population models where systematic random immigration events promoting growth are simultaneously balanced with random emigration ones provoking thinning. The origin of mass removals are either determined by external demands or by aging leading to different conditions of stability.

Citations

• Singularity Analysis of Generating Functions
• Modified Galton-Watson processes with immigration under an alternative offspring mechanism

Related

• Equilibrium Equations for Human Populations with Immigration
• Branching processes in random environment with immigration stopped at zero
• Strong Allee Effect in A Stochastic Logistic Model with Mate Limitation and Stochastic Immigration
• Simple tools for extrapolations of human mortality in rich countries
• On Time-Changed Linear Birth-Death Process with Immigration at Extinction