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- W3185174920 abstract "Given a locally finite graph $Gamma$, an amenable subgroup $G$ of graph automorphisms acting freely and almost transitively on its vertices, and a $G$-invariant activity function $lambda$, consider the free energy $f_G(Gamma,lambda)$ of the hardcore model defined on the set of independent sets in $Gamma$ weighted by $lambda$. We define suitable ensembles of hardcore models and prove that, under some recursion-theoretic assumptions on $G$, if $|lambda|_infty lambda_c(Delta)$, there is no such algorithm, unless $mathrm{NP} = mathrm{RP}$, where $lambda_c(Delta)$ denotes the critical activity on the $Delta$-regular tree. This recovers the computational phase transition for the partition function of the hardcore model on finite graphs and provides an extension to the infinite setting. As an application in symbolic dynamics, we use these results to develop efficient approximation algorithms for the topological entropy of subshifts of finite type with enough safe symbols, we obtain a representation formula of topological entropy in terms of random trees of self-avoiding walks, and we provide new conditions for the uniqueness of the measure of maximal entropy based on the connective constant of a particular associated graph." @default.
- W3185174920 created "2021-08-02" @default.
- W3185174920 creator A5018537690 @default.
- W3185174920 date "2021-07-29" @default.
- W3185174920 modified "2023-10-06" @default.
- W3185174920 title "Counting independent sets in amenable graphs" @default.
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