On large‐girth regular graphs and random processes on trees | Zendy

Backhausz Ágnes | Zendy; Szegedy Balázs | Zendy

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On large‐girth regular graphs and random processes on trees

Author(s) -

Backhausz Ágnes,

Szegedy Balázs

Publication year - 2018

Publication title -

random structures and algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.314

H-Index - 69

eISSN - 1098-2418

pISSN - 1042-9832

DOI - 10.1002/rsa.20769

Subject(s) - mathematics , markov chain , automorphism group , glauber , combinatorics , discrete mathematics , invariant (physics) , tree (set theory) , class (philosophy) , branching (polymer chemistry) , automorphism , computer science , statistics , physics , scattering , optics , mathematical physics , materials science , composite material , artificial intelligence

We study various classes of random processes defined on the regular tree T d that are invariant under the automorphism group of T d . The most important ones are factor of i.i.d. processes (randomized local algorithms), branching Markov chains and a new class that we call typical processes. Using Glauber dynamics on processes we give a sufficient condition for a branching Markov chain to be factor of i.i.d.

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