We prove that a supercritical branching random walk on a transient Markov chain converges almost surely under rescaling to a random measure on the Martin boundary of the underlying Markov chain. Several open problems and conjectures about this limiting measure are presented.
Candellero, E., Hutchcroft, T. (2023). On the boundary at infinity for branching random walk. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 28, 1-12 [10.1214/23-ECP560].
On the boundary at infinity for branching random walk
Elisabetta Candellero
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2023-01-01
Abstract
We prove that a supercritical branching random walk on a transient Markov chain converges almost surely under rescaling to a random measure on the Martin boundary of the underlying Markov chain. Several open problems and conjectures about this limiting measure are presented.File in questo prodotto:
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