The Large Deviation Principle for Interacting Dynamical Systems on Random Graphs
Sign Up to like & getrecommendations! Published in 2022 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-022-04312-1
Abstract: Using the weak convergence approach to large deviations, we formulate and prove the large deviation principle (LDP) for W-random graphs in the cut-norm topology. This generalizes the LDP for Erdős-R{\' e}nyi random graphs by Chatterjee… read more here.
Keywords: principle; dynamical systems; large deviation; random graphs ... See more keywords
Large Deviations in Generalized Random Graphs with Node Weights
Sign Up to like & getrecommendations! Published in 2018 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-018-7357-6
Abstract: Generalized random graphs are considered where the presence or absence of an edge depends on the weights of its nodes. Our main interest is to investigate large deviations for the number of edges per node… read more here.
Keywords: generalized random; random graphs; large deviations; node weights ... See more keywords
Cluster Tails for Critical Power-Law Inhomogeneous Random Graphs
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Statistical Physics"
DOI: 10.1007/s10955-018-1978-0
Abstract: Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299–2361, 2012). It was… read more here.
Keywords: random graphs; cluster; inhomogeneous random; power law ... See more keywords
Large Deviations for the Annealed Ising Model on Inhomogeneous Random Graphs: Spins and Degrees
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DOI: 10.1007/s10955-018-2027-8
Abstract: We prove a large deviations principle for the total spin and the number of edges under the annealed Ising measure on generalized random graphs. We also give detailed results on how the annealing over the… read more here.
Keywords: random graphs; ising model; annealed ising; large deviations ... See more keywords
The minrank of random graphs over arbitrary fields
Sign Up to like & getrecommendations! Published in 2019 at "Israel Journal of Mathematics"
DOI: 10.1007/s11856-019-1945-8
Abstract: The minrank of a graph G on the set of vertices [ n ] over a field $$\mathbb{F}$$ F is the minimum possible rank of a matrix $$M \in \mathbb{F}^{{n}\times{n}}$$ M ∈ F n ×… read more here.
Keywords: minrank random; graphs arbitrary; field; random graphs ... See more keywords
HyGen: generating random graphs with hyperbolic communities
Sign Up to like & getrecommendations! Published in 2019 at "Applied Network Science"
DOI: 10.1007/s41109-019-0166-8
Abstract: Random graph generators are necessary tools for many network science applications. For example, the evaluation of graph analysis algorithms requires methods for generating realistic synthetic graphs. Typically random graph generators are generating graphs that satisfy… read more here.
Keywords: graphs hyperbolic; community; random graphs; graph ... See more keywords
Spectral bounds in random graphs applied to spreading phenomena and percolation
Sign Up to like & getrecommendations! Published in 2018 at "Advances in Applied Probability"
DOI: 10.1017/apr.2018.22
Abstract: Abstract In this paper we derive nonasymptotic upper bounds for the size of reachable sets in random graphs. These bounds are subject to a phase transition phenomenon triggered by the spectral radius of the hazard… read more here.
Keywords: graphs applied; percolation; bounds random; random graphs ... See more keywords
Speeding up non-Markovian first-passage percolation with a few extra edges
Sign Up to like & getrecommendations! Published in 2018 at "Advances in Applied Probability"
DOI: 10.1017/apr.2018.39
Abstract: Abstract One model of real-life spreading processes is that of first-passage percolation (also called the SI model) on random graphs. Social interactions often follow bursty patterns, which are usually modelled with independent and identically distributed… read more here.
Keywords: random graphs; first passage; passage; passage percolation ... See more keywords
The sharp threshold for jigsaw percolation in random graphs
Sign Up to like & getrecommendations! Published in 2019 at "Advances in Applied Probability"
DOI: 10.1017/apr.2019.24
Abstract: Abstract We analyse the jigsaw percolation process, which may be seen as a measure of whether two graphs on the same vertex set are ‘jointly connected’. Bollobás, Riordan, Slivken, and Smith (2017) proved that, when… read more here.
Keywords: random graphs; jigsaw; jigsaw percolation;
Inhomogeneous random graphs, isolated vertices, and Poisson approximation
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Applied Probability"
DOI: 10.1017/jpr.2018.9
Abstract: Abstract Consider a graph on randomly scattered points in an arbitrary space, with any two points x, y connected with probability ϕ(x, y). Suppose the number of points is large but the mean number of… read more here.
Keywords: random graphs; number; graphs isolated; inhomogeneous random ... See more keywords
On connectivity and robustness of random graphs with inhomogeneity
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Applied Probability"
DOI: 10.1017/jpr.2022.32
Abstract: Abstract The study of threshold functions has a long history in random graph theory. It is known that the thresholds for minimum degree k, k-connectivity, as well as k-robustness coincide for a binomial random graph.… read more here.
Keywords: random; random graphs; connectivity robustness;