Displaying similar documents to “Rapid mixing of Swendsen-Wang dynamics in two dimensions”

Spectral gap for an unrestricted Kawasaki type dynamics

Gustavo Posta (2010)

ESAIM: Probability and Statistics

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We give an accurate asymptotic estimate for the gap of the generator of a particular interacting particle system. The model we consider may be informally described as follows. A certain number of charged particles moves on the segment [1,L] according to a Markovian law. One unitary charge, positive or negative, jumps from a site k to another site k'=k+1 or k'=k-1 at a rate which depends on the charge at site k and at site k'. The total charge of the system is preserved by the...

Matrix and discrepancy view of generalized random and quasirandom graphs

Marianna Bolla, Ahmed Elbanna (2016)

Special Matrices

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We will discuss how graph based matrices are capable to find classification of the graph vertices with small within- and between-cluster discrepancies. The structural eigenvalues together with the corresponding spectral subspaces of the normalized modularity matrix are used to find a block-structure in the graph. The notions are extended to rectangular arrays of nonnegative entries and to directed graphs. We also investigate relations between spectral properties, multiway discrepancies,...

Asymptotic properties of random graphs

Zbigniew Palka

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CONTENTS1. Introduction...........................................................................5  1.1. Purpose and scope..........................................................5  1.2. Probability-theoretic preliminaries....................................6  1.3. Graphs............................................................................11  1.4. Random graphs..............................................................132. Vertex-degrees....................................................................15  2.1....

Multilevel Modeling of the Forest Resource Dynamics

I. N. Vladimirov, A. K. Chudnenko (2009)

Mathematical Modelling of Natural Phenomena

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We examine the theoretical and applications-specific issues relating to modeling the temporal and spatial dynamics of forest ecosystems, based on the principles of investigating dynamical models. When developing the predictive dynamical models of forest resources, there is a possibility of achieving uniqueness of the solutions to equations by taking into account the initial and boundary conditions of the solution, and the conditions of the geographical environment. We present the results...

Mixing time for the Ising model : a uniform lower bound for all graphs

Jian Ding, Yuval Peres (2011)

Annales de l'I.H.P. Probabilités et statistiques

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Consider Glauber dynamics for the Ising model on a graph of vertices. Hayes and Sinclair showed that the mixing time for this dynamics is at least log /(), where is the maximum degree and () = (log2). Their result applies to more general spin systems, and in that generality, they showed that some dependence on is necessary. In this paper, we focus on the ferromagnetic Ising model and prove that the mixing time of Glauber dynamics on any -vertex graph is at least (1/4 + o(1))log . ...

Asymptotic spectral analysis of generalized Erdős-Rényi random graphs

Song Liang, Nobuaki Obata, Shuji Takahashi (2007)

Banach Center Publications

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Motivated by the Watts-Strogatz model for a complex network, we introduce a generalization of the Erdős-Rényi random graph. We derive a combinatorial formula for the moment sequence of its spectral distribution in the sparse limit.