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Typicality and entropy of processes on infinite trees
Multi angle
Authors : Backhausz, Agnes (Author of the conference)
CIRM (Publisher )
05C80 - Random graphs
28D20 - Entropy and other invariants
37A35 - Entropy and other invariants, isomorphism, classification
CIRM (Publisher )
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Abstract :
We consider a special family of invariant random processes on the infinite d-regular tree, which is closely related to random d-regular graphs, and helps understanding the structure of these finite objects. By using different notions of entropy and finding inequalities between these quantities, we present a sufficient condition for a process to be typical, that is, to be the weak local limit of functions on the vertices of a randomly chosen d-regular graph (with fixed d, and the number of vertices tending to infinity). Our results are based on invariant couplings of the process with another copy of itself. The arguments can also be extended to processes on unimodular Galton-Watson trees. In the talk we present the notion of typicality, the entropy inequalities that we use and the sufficient conditions mentioned above. Joint work with Charles Bordenave and Balázs Szegedy.
Keywords : infinite trees; invariant process; sofic entropy
MSC Codes : Keywords : infinite trees; invariant process; sofic entropy
05C80 - Random graphs
28D20 - Entropy and other invariants
37A35 - Entropy and other invariants, isomorphism, classification
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Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 09/06/2023 Conference Date : 22/05/2023 Subseries : Research talks arXiv category : Probability Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:49:39 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-05-22_Backhausz.mp4 
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Information on the Event
Event Title : Measured Group Theory, Stochastic Processes on Groups and Borel Combinatorics / Théorie mesurée des groupes, processus stochastiques sur les groupes et combinatoire BorélienneEvent Organizers : Abért, Miklós ; Gaboriau, Damien ; Tserunyan, Anush ; Virág, Bálint Dates : 22/05/2023 - 26/05/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2172.html
Citation Data
DOI : 10.24350/CIRM.V.20048403Cite this video as: Backhausz, Agnes (2023). Typicality and entropy of processes on infinite trees. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20048403 URI : http://dx.doi.org/10.24350/CIRM.V.20048403 |
See Also
- [Multi angle] Treeability and planarity in measured group theory / Author of the conference Tucker-Drob, Robin.
- [Multi angle] Commability and graphs of abelian groups / Author of the conference Le Boudec, Adrien.
- [Multi angle] Borel asymptotic dimension and hyperfiniteness / Author of the conference Conley, Clinton.
- [Multi angle] Perfect kernels and dynamics: from Bass-Serre theory to hyperbolic groups / Author of the conference Azuelos, Pénélope.
Bibliography
- BACKHAUSZ, Agnes, BORDENAVE, Charles, et SZEGEDY, Balázs. Typicality and entropy of processes on infinite trees. In : Annales de l'Institut Henri Poincare (B) Probabilites et statistiques. Institut Henri Poincaré, 2022. p. 1959-1980. - http://dx.doi.org/10.1214/21-AIHP1233
- BACKHAUSZ, Agnes et SZEGEDY, Balázs. On large‐girth regular graphs and random processes on trees. Random Structures & Algorithms, 2018, vol. 53, no 3, p. 389-416. - https://doi.org/10.1002/rsa.20769
- NAM, Danny, SLY, Allan, et ZHANG, Lingfu. Ising model on trees and factors of IID. Communications in Mathematical Physics, 2022, p. 1-38. - http://dx.doi.org/10.1007/s00220-021-04260-2
- RAHMAN, Mustazee et VIRAG, Bálint. Local algorithms for independent sets are half-optimal. Ann. Probab. 2017. 45 (3) 1543 - 1577 - http://dx.doi.org/10.1214/16-AOP1094
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