Typicality and entropy of processes on infinite trees | Vidéo | Carmin.tv

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Typicality and entropy of processes on infinite trees

By Ágnes Backhausz

Appears in collection : Measured Group Theory, Stochastic Processes on Groups and Borel Combinatorics / Théorie mesurée des groupes, processus stochastiques sur les groupes et combinatoire Borélienne

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.

Information about the video

Date of recording 22/05/2023
Date of publication 09/06/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Jean Petit
Format MP4

Citation data

DOI 10.24350/CIRM.V.20048403
Cite this video Backhausz, Ágnes (22/05/2023). Typicality and entropy of processes on infinite trees. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20048403
URL https://dx.doi.org/10.24350/CIRM.V.20048403

Domain(s)

Probability

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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