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Ising models on locally tree-like graphs
Ising model random sparse graphs cavity method Bethe measures belief propagation local weak convergence
2015/8/21
We consider Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the...
The weak limit of Ising models on locally tree-like graphs
Ising model the temperature the last beta sequence
2015/8/20
We consider the Ising model with inverse temperature β and without external field on sequences of graphs Gn which converge locally to the k-regular tree. We show that for such graphs the Ising m...
FACTOR MODELS ON LOCALLY TREE-LIKE GRAPHS
Factor models random graphs belief propagation Bethe measures Potts model independent set Gibbs measures free energy density local weak convergence
2015/8/20
We consider homogeneous factor models on uniformly sparse graph sequences converg-ing locally to a (unimodular) random tree T, and study the existence of the free energy density ,the limit of the log...
GRAPH LIMITS AND EXCHANGEABLE RANDOM GRAPHS
Figure restrictions and can exchange random graph
2015/7/8
GRAPH LIMITS AND EXCHANGEABLE RANDOM GRAPHS。
A SEQUENTIAL IMPORTANCE SAMPLING ALGORITHM FOR GENERATING RANDOM GRAPHS WITH PRESCRIBED DEGREES
Sequential sampling algorithms the random graph degree
2015/7/8
A SEQUENTIAL IMPORTANCE SAMPLING ALGORITHM FOR GENERATING RANDOM GRAPHS WITH PRESCRIBED DEGREES。
A Mermin--Wagner theorem for quantum Gibbs states on 2D graphs, I
quantum bosonic system with continuous spins symmetry group the Feynman–Kac representation bi-dimensional graphs Gibbs states
2012/6/25
This is the the first of a series of papers considering properties of quantum systems over 2D graphs or manifolds, with continuous spins. In the model considered here the phase space of a single spin ...
For a graph $G$, denote by $t(G)$ (resp. $b(G)$) the maximum size of a triangle-free (resp. bipartite) subgraph of $G$. Of course $t(G) \geq b(G)$ for any $G$, and a classic result of Mantel from 1907...
Cover times for sequences of Markov chains on random graphs
Random walk Cover time Maximal hitting time Random graph
2012/6/15
We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (type 1) is the class of cover times approximated by the maximal hitting times s...
Connectivity Threshold of Random Geometric Graphs with Cantor Distributed Vertices
Cantor distribution connectivity threshold random geometric graph singular distributions
2012/4/18
For connectivity of \emph{random geometric graphs}, where there is no density for underlying distribution of the vertices, we consider $n$ i.i.d. \emph{Cantor} distributed points on $[0,1]$. We show t...
Bond percolation on isoradial graphs
Bond percolation isoradial graph rhombic tiling Penrose tiling inhomogeneous percolation universality
2012/4/18
In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for h...
Stochastic Service Systems, Random Interval Graphs and Search Algorithms
Queueing theory interval graphs Lambert series asymptotic expansions
2011/9/15
Abstract: We consider several stochastic service systems, and study the asymptotic behavior of the moments of various quantities that have application to models for random interval graphs and algorith...
Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on Z^2
Uniform spanning tree loop-erased random walk abelian sandpile model
2011/9/14
Abstract: We show how to compute the probabilities of various connection topologies for uniformly random spanning trees on graphs embedded in surfaces. As an application, we show how to compute the "i...
Asymptotics of first-passage percolation on 1-dimensional graphs
Asymptotics of first-passage percolation 1-dimensional graphs Probability
2011/9/2
Abstract: In this paper we consider standard first-passage percolation on certain 1-dimensional periodic graphs. One such graph of particular interest is the $\Z\times\{0,1,...,K-1\}^{d-1}$ nearest ne...
Robustness of Two Simple Rules for the Evolution of Cooperation on Regular Graphs
Evolutionary game theory evolution of cooperation interacting particle systems voter model perturbations voter model
2011/8/29
Abstract: We study two simple rules on finite graphs for the death-birth updating and the imitation updating discovered by Ohtsuki, Hauert, Lieberman, and Nowak [\emph{Nature} {\bf 441} (2006) 502-505...
Extremal results regarding $K_6$-minors in graphs of girth at least 5
Extremal results regarding $K_6$-minors graphs of girth
2011/2/28
We prove that every 6-connected graph of girth ≥ 6 has a K6-minor and thus settle Jorgensen’s
conjecture for graphs of girth ≥ 6. Relaxing the assumption on the girth, we prove that every
6-connecte...