Spectral measures of factor of i.i.d. processes on vertex-transitive graphs

Backhausz, Ágnes; Virág, Bálint

doi:10.1214/16-aihp790

Cited by 15 publications

(11 citation statements)

References 31 publications

(44 reference statements)

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“…The general necessary condition on factor of i.i.d. covariance structures is not sufficient for a branching Markov chain. To show this, we use our necessary conditions for typical processes (Section 4), which automatically apply for factor of i.i.d.…”

Section: Introductionmentioning

confidence: 99%

On large‐girth regular graphs and random processes on trees

Backhausz

Szegedy

2018

Random Struct Algorithms

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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. K E Y W O R D Sfactor of i.i.d.

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Section: Introductionmentioning

confidence: 99%

On large‐girth regular graphs and random processes on trees

Backhausz

Szegedy

2018

Random Struct Algorithms

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“…• The average correlation is bounded by the spectral radius of the adjacency operator divided by d. This follows from the results of [6] on the covariance structure of factor-of-IID processes. • By a Cheeger-tpye inequality [23,Theorem 6.7], the spectral radius is bounded by…”

Section: Beyond Entropy: Possible Generalizationsmentioning

confidence: 94%

Entropy and expansion

Csóka¹,

Harangi²,

Virág³

2020

Ann. Inst. H. Poincaré Probab. Statist.

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Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of independent random seeds. The inequality involves a constant characterizing the expansion properties of the system.Our results generalize to entropy inequalities used in recent work in invariant settings, including the edge-vertex inequality for factor-of-IID processes, Bowen's entropy inequalities, and Bollobás's entropy bounds in random regular graphs.The proof method yields inequalities for other measures of randomness, including covariance.As an application, we give upper bounds for independent sets in both finite and infinite graphs.

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“…Correlation bounds provide further necessary conditions [5]: this is the main tool in the current paper as well. In [4] the possible 'correlation structures' were described for factor of i.i.d. processes by understanding their spectral measures.…”

Section: Related Workmentioning

confidence: 99%

Correlation Bounds for Distant Parts of Factor of IID Processes

Backhausz¹,

Gerencsér²,

Harangi³

et al. 2017

Combinator. Probab. Comp.

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We study factor of i.i.d. processes on the d-regular tree for d 3. We show that if such a process is restricted to two distant connected subgraphs of the tree, then the two parts are basically uncorrelated. More precisely, any functions of the two parts have correlation at most k(d − 1)/( √ d − 1) k , where k denotes the distance between the subgraphs. This result can be considered as a quantitative version of the fact that factor of i.i.d. processes have trivial 1-ended tails.

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Spectral measures of factor of i.i.d. processes on vertex-transitive graphs

Cited by 15 publications

References 31 publications

On large‐girth regular graphs and random processes on trees

On large‐girth regular graphs and random processes on trees

Entropy and expansion

Correlation Bounds for Distant Parts of Factor of IID Processes

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