Branching random walks and Martin boundaries: some properties, examples and counterexamples | Vidéo | Carmin.tv

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Branching random walks and Martin boundaries: some properties, examples and counterexamples

By Elisabetta Candellero

Appears in collection : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiens

Let $G$ be an infinite locally finite and transitive graph. We investigate the relation between supercritical transient branching random walk (BRW) and the Martin boundary of its underlying random walk. We show results regarding the typical (and some atypical) asymptotic directions taken by the particles. We focus on the behavior of BRW inside given subgraphs by putting into relation geometrical properties of the subgraph itself and the behavior of BRW on it. We will also present some examples and counter examples. (Based on joint works with T. Hutchcroft,D. Bertacchi and F. Zucca.)

Information about the video

Date of recording 06/10/2023
Date of publication 23/10/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20098203
Cite this video Candellero, Elisabetta (06/10/2023). Branching random walks and Martin boundaries: some properties, examples and counterexamples. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20098203
URL https://dx.doi.org/10.24350/CIRM.V.20098203

Domain(s)

Probability

Bibliography

CANDELLERO, Elisabetta et HUTCHCROFT, Tom. On the boundary at infinity for branching random walk. arXiv preprint arXiv:2205.15287, 2022. - https://doi.org/10.48550/arXiv.2205.15287
BERTACCHI, Daniela, CANDELLERO, Elisabetta, et ZUCCA, Fabio. Martin boundaries and asymptotic behavior of branching random walks. arXiv preprint arXiv:2308.03711, 2023. - https://doi.org/10.48550/arXiv.2308.03711

MSC codes

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