English
Parking on the infinite binary tree
Multi angle
Auteurs : Contat, Alice (Auteur de la conférence)
CIRM (Editeur )
60C05 - Combinatorial probability
60K35 - Interacting random processes; statistical mechanics type models; percolation theory
82B27 - Critical phenomena
CIRM (Editeur )
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Résumé :
Consider a rooted tree whose vertices will be interpreted as free parking spots, each spot accommodating at most one car. On top of that tree, we consider a non-negative integer labeling representing the number of cars arriving on each vertex. Each car tries to park on its arrival vertex, and if the spot is occupied, it travels downwards in direction of the root of the tree until it finds an empty vertex to park. If there is no such vertex on the path towards the root, the car exits the tree, contributing to the flux of cars at the root. This models undergoes an interesting phase transition which we will analyze in detail. After an overview of the case where the underlying tree is a critical Bienayme-Galton-Watson tree, we will concentrate on the case where the underlying tree is the in finite binary tree, where the phase transition turns out to be "discontinuous".
The talk is based on a joint work with David Aldous, Nicolas Curien and Olivier Hénard.
Mots-Clés : parking process; infinite binary tree; phase transition
Codes MSC : The talk is based on a joint work with David Aldous, Nicolas Curien and Olivier Hénard.
Mots-Clés : parking process; infinite binary tree; phase transition
60C05 - Combinatorial probability
60K35 - Interacting random processes; statistical mechanics type models; percolation theory
82B27 - Critical phenomena
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 23/10/2023 Date de Captation : 02/10/2023 Sous Collection : Research talks Catégorie arXiv : Probability ; Combinatorics Domaine(s) : Combinatoires ; Probabilités & Statistiques Format : MP4 (.mp4) - HD Durée : 00:50:44 Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-10-02_Contat.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 de la Rencontre : https://conferences.cirm-math.fr/2897.html
Données de citation
DOI : 10.24350/CIRM.V.20098503Citer cette vidéo: Contat, Alice (2023). Parking on the infinite binary tree. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20098503 URI : http://dx.doi.org/10.24350/CIRM.V.20098503 |
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Bibliographie
- ALDOUS, David, CONTAT, Alice, CURIEN, Nicolas, et al. Parking on the infinite binary tree. Probability Theory and Related Fields, 2023, p. 1-24. - https://doi.org/10.1007/s00440-023-01189-6
- CONTAT, Alice et CURIEN, Nicolas (2021). Parking on Cayley trees & Frozen Erdös-Rényi. The Annals of Probability, to appear. -
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