The number of ends of critical branching random walks
Elisabetta Candellero, Matthew I. Roberts
TL;DR
This paper studies the topological ends of the trace of branching random walks on graphs, providing conditions for infinitely many ends and examples with only one end, advancing understanding of their topological structure.
Contribution
It offers a new sufficient condition for the trace of a BRW to have infinitely many ends and presents examples of non-symmetric BRWs with a single end.
Findings
Sufficient condition for infinitely many ends of BRW trace
Examples of non-symmetric BRWs with one end
Enhanced understanding of topological structure of BRW traces
Abstract
We investigate the number of topological ends of the trace of branching random walk (BRW) on a graph, giving a sufficient condition for the trace to have infinitely many ends. We then describe some interesting examples of non-symmetric BRWs with just one end.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods · Topological and Geometric Data Analysis