Characterization of the Critical Values of Branching Random Walks on Weighted Graphs through Infinite-type Branching Processes
نویسنده
چکیده
We study the branching random walk on weighted graphs; site-breeding and edgebreeding branching random walks on graphs are seen as particular cases. We describe the strong critical value in terms of a geometrical parameter of the graph. We characterize the weak critical value and relate it to another geometrical parameter. We prove that, at the strong critical value, the process dies out locally almost surely; while, at the weak critical value, global survival and global extinction are both possible.
منابع مشابه
Characterization of Critical Values of Branching Random Walks on Weighted Graphs through Infinite-type Branching Processes
We study the branching random walk on weighted graphs; site-breeding and edgebreeding branching random walks on graphs are seen as particular cases. Two kinds of survival can be identified: a weak survival (with positive probability there is at least one particle alive somewhere at any time) and a strong survival (with positive probability the colony survives by returning infinitely often to a ...
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