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.
Funding Statement
TH was partially supported by ERC starting grant 804166 (SPRS). EC was supported by the project “Programma per Giovani Ricercatori Rita Levi Montalcini” awarded by the Italian Ministry of Education. EC acknowledges partial support by “INdAM–GNAMPA Project 2019” and “INdAM–GNAMPA Project 2020”.
Acknowledgments
This work was initiated while TH was a senior research associate at the University of Cambridge, during which time he was supported by ERC starting grant 804166 (SPRS). EC was supported by the project “Programma per Giovani Ricercatori Rita Levi Montalcini” awarded by the Italian Ministry of Education. EC also acknowledges partial support by “INdAM–GNAMPA Project 2019” and “INdAM–GNAMPA Project 2020”.
Citation
Elisabetta Candellero. Tom Hutchcroft. "On the boundary at infinity for branching random walk." Electron. Commun. Probab. 28 1 - 12, 2023. https://doi.org/10.1214/23-ECP560
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