Continuum Cascade Model: Branching Random Walk for Traveling Wave

2015/07/15 by Yoshiaki Itoh, Itoh, Yoshiaki
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.1507.04379

arXiv admin note: text overlap with arXiv:1206.3711; and text overlap with arXiv:1101.1810 by other authors

openalex publication_date 2015/07/15 · arxiv created 2018/08/02 · arxiv updated 2018/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The food web is a directed graph in which nodes label species and directed links represent the predation between species. The cascade model generates random food webs. The continuum cascade model is a Poisson approximation of the cascade model. The recursion to obtain the probability distribution of the longest chain length generated by the continuum cascade model has the solution with traveling wave. We consider a branching random walk to study the asymptotic probability on the position of wave front.

Citations

• Continuum Cascade Model of Directed Random Graphs: Traveling Wave Analysis
• Convergence in law of the minimum of a branching random walk

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