arXiv subjects

András Mészáros

Publications and source records attributed to András Mészáros.

24 records · Page 2Linked to original sources

arXiv2020

On the free energy density of factor models on biregular graphs

Let $h(0),h(1),\dots,h(k)$ be a symmetric concave sequence. For a $(d,k)$-biregular factor graph $G$ and $x\in \{0,1\}^V$, we define the Hamiltonian \[H_G(x)=\sum_{f\in F} h\left(\sum_{v\in \partial f} x_v\right),\] where $V$ is the set of variable nodes, $F$ is the set of factor nodes. We prove that if $(G_n)$ is a large girth sequence of $(d,k)$-biregular factor graphs, then the free energy density of $G_n$ converges. The limiting free energy density is given by the Bethe-approximation.

math.CO↗

arXiv2020

A BK inequality for random matchings

Let $G=(S,T,E)$ be a bipartite graph. For a matching $M$ of $G$, let $V(M)$ be the set of vertices covered by $M$, and let $B(M)$ be the symmetric difference of $V(M)$ and $S$. We prove that if $M$ is a uniform random matching of $G$, then $B(M)$ satisfies the BK inequality for increasing events.

math.CO↗

arXiv2020

Atoms of the matching measure

We prove that the matching measure of an infinite vertex-transitive connected graph has no atoms. Generalizing the results of Salez, we show that for an ergodic non-amenable unimodular random rooted graph with uniformly bounded degrees, the matching measure has only finitely many atoms. Ku and Chen proved the analogue of the Gallai-Edmonds structure theorem for non-zero roots of the matching polynomial for finite graphs. We extend their results for infinite graphs. We also show that the corresponding Gallai-Edmonds decomposition is compatible with the zero temperature monomer-dimer model.

math.PR↗

arXiv2020

Limiting entropy of determinantal processes

We extend Lyons's tree entropy theorem to general determinantal measures. As a byproduct we show that the sofic entropy of an invariant determinantal measure does not depend on the chosen sofic approximation.

math.PR↗

arXiv2020

The distribution of sandpile groups of random regular graphs

We study the distribution of the sandpile group of random d-regular graphs. For the directed model, we prove that it follows the Cohen-Lenstra heuristics, that is, the limiting probability that the $p$-Sylow subgroup of the sandpile group is a given $p$-group $P$, is proportional to $|Aut(P)|^{-1}$. For finitely many primes, these events get independent in the limit. Similar results hold for undirected random regular graphs, where for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne. This answers an open question of Frieze and Vu whether the adjacency matrix of a random regular graph is invertible with high probability. Note that for directed graphs this was recently proved by Huang. It also gives an alternate proof of a theorem of Backhausz and Szegedy.

math.CO↗

arXiv2019

Multi timescale bandwidth profile and its application for burst-aware fairness

We propose a resource sharing scheme that takes into account the traffic history over several predefined time scales and provides fair resource sharing considering the traffic history. Our concept builds on a simplified version of core-stateless resource sharing, where we only use a few Drop Precedences (DPs). For packet marking we introduce Multi timescale bandwidth profile. Additionally, we provide basic dimensioning concepts for the proposed schema and present its simulation based performance analysis.

cs.NI↗