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Branching random walks and Martin boundaries: some properties, examples and counterexamples
Multi angle
Authors : Candellero, Elisabetta (Author of the conference)
CIRM (Publisher )
60J10 - Markov chains (discrete-time Markov processes on discrete state spaces)
60J45 - Probabilistic potential theory
60J80 - Branching processes (Galton-Watson, birth-and-death, etc.)
CIRM (Publisher )
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Abstract :
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.)
Keywords : branching random walk; Martin boundary; random walk; persistence; survival; tree
MSC Codes : Keywords : branching random walk; Martin boundary; random walk; persistence; survival; tree
60J10 - Markov chains (discrete-time Markov processes on discrete state spaces)
60J45 - Probabilistic potential theory
60J80 - Branching processes (Galton-Watson, birth-and-death, etc.)
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 23/10/2023 Conference Date : 06/10/2023 Subseries : Research talks arXiv category : Probability Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:52:09 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-10-06_Candellero.mp4 
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Information on the Event
Event Title : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiensEvent Organizers : Curien, Nicolas ; Garcia-Failde, Elba ; Petri, Bram ; Singh, Arvind Dates : 02/10/2023 - 06/10/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2897.html
Citation Data
DOI : 10.24350/CIRM.V.20098203Cite this video as: Candellero, Elisabetta (2023). Branching random walks and Martin boundaries: some properties, examples and counterexamples. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20098203 URI : http://dx.doi.org/10.24350/CIRM.V.20098203 |
See Also
- [Multi angle] On the length spectrum of random hyperbolic 3-manifolds / Author of the conference Roig Sanchis, Anna.
- [Multi angle] Crossing the line: from graphs to curves / Author of the conference Parlier, Hugo.
- [Multi angle] Hyperbolic Voronoi percolation / Author of the conference Müller, Tobias.
- [Multi angle] Tail bounds for detection times in mobile hyperbolic graphs / Author of the conference Mitsche, Dieter.
- [Multi angle] Combinatorial maps and hyperbolic surfaces in high genus / Author of the conference Louf, Baptiste.
- [Multi angle] Irreducibility of random polynomials / Author of the conference Kozma, Gady.
- [Multi angle] Non-perturbative topological recursion and Weil-Petersson volumes / Author of the conference Gregori, Paolo.
- [Multi angle] Geometry of large genus flat surfaces / Author of the conference Goujard, Élise.
- [Multi angle] Resurgent large genus asymptotics of intersection numbers / Author of the conference Giacchetto, Alessandro.
- [Multi angle] Integration on Grassmannians and deformed monotone Hurwitz numbers / Author of the conference Do, Norman.
- [Multi angle] Parking on the infinite binary tree / Author of the conference Contat, Alice.
- [Multi angle] Distances and isoperimetric inequalities in random maps of large genus / Author of the conference Chapuy, Guillaume.
- [Multi angle] The geometry of random genus-0 hyperbolic surfaces via trees / Author of the conference Budd, Timothy.
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
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