English
Branching random walks and Martin boundaries: some properties, examples and counterexamples
Multi angle
Auteurs : Candellero, Elisabetta (Auteur de la Conférence)
CIRM (Editeur )
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 (Editeur )
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Résumé :
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
Codes MSC : 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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Informations sur la Vidéo
Réalisateur : Recanzone, LucaLangue : Anglais Date de publication : 23/10/2023 Date de captation : 06/10/2023 Sous collection : Research talks arXiv category : Probability Domaine : Probability & Statistics Format : MP4 (.mp4) - HD Durée : 00:52:09 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-10-06_Candellero.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiensOrganisateurs de la rencontre : Curien, Nicolas ; Garcia-Failde, Elba ; Petri, Bram ; Singh, Arvind Dates : 02/10/2023 - 06/10/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2897.html
Données de citation
DOI : 10.24350/CIRM.V.20098203Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] On the length spectrum of random hyperbolic 3-manifolds / Auteur de la Conférence Roig Sanchis, Anna.
- [Multi angle] Crossing the line: from graphs to curves / Auteur de la Conférence Parlier, Hugo.
- [Multi angle] Hyperbolic Voronoi percolation / Auteur de la Conférence Müller, Tobias.
- [Multi angle] Tail bounds for detection times in mobile hyperbolic graphs / Auteur de la Conférence Mitsche, Dieter.
- [Multi angle] Combinatorial maps and hyperbolic surfaces in high genus / Auteur de la Conférence Louf, Baptiste.
- [Multi angle] Irreducibility of random polynomials / Auteur de la Conférence Kozma, Gady.
- [Multi angle] Non-perturbative topological recursion and Weil-Petersson volumes / Auteur de la Conférence Gregori, Paolo.
- [Multi angle] Geometry of large genus flat surfaces / Auteur de la Conférence Goujard, Élise.
- [Multi angle] Resurgent large genus asymptotics of intersection numbers / Auteur de la Conférence Giacchetto, Alessandro.
- [Multi angle] Integration on Grassmannians and deformed monotone Hurwitz numbers / Auteur de la Conférence Do, Norman.
- [Multi angle] Parking on the infinite binary tree / Auteur de la Conférence Contat, Alice.
- [Multi angle] Distances and isoperimetric inequalities in random maps of large genus / Auteur de la Conférence Chapuy, Guillaume.
- [Multi angle] The geometry of random genus-0 hyperbolic surfaces via trees / Auteur de la Conférence Budd, Timothy.
Bibliographie
- 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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