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Parking on the infinite binary tree
Multi angle
Authors : Contat, Alice (Author of the conference)
CIRM (Publisher )
60C05 - Combinatorial probability
60K35 - Interacting random processes; statistical mechanics type models; percolation theory
82B27 - Critical phenomena
CIRM (Publisher )
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Abstract :
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.
Keywords : parking process; infinite binary tree; phase transition
MSC Codes : The talk is based on a joint work with David Aldous, Nicolas Curien and Olivier Hénard.
Keywords : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/10/2023 Conference Date : 02/10/2023 Subseries : Research talks arXiv category : Probability ; Combinatorics Mathematical Area(s) : Combinatorics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:50:44 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-10-02_Contat.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.20098503Cite this video as: 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 |
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] Distances and isoperimetric inequalities in random maps of large genus / Author of the conference Chapuy, Guillaume.
- [Multi angle] Branching random walks and Martin boundaries: some properties, examples and counterexamples / Author of the conference Candellero, Elisabetta.
- [Multi angle] The geometry of random genus-0 hyperbolic surfaces via trees / Author of the conference Budd, Timothy.
Bibliography
- 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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