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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.