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[ספר][B] Gibbs measures on Cayley trees
UA Rozikov - 2013 - books.google.com
The purpose of this book is to present systematically all known mathematical results on
Gibbs measures on Cayley trees (Bethe lattices). The Gibbs measure is a probability …
Gibbs measures on Cayley trees (Bethe lattices). The Gibbs measure is a probability …
[ספר][B] Progress in high-dimensional percolation and random graphs
M Heydenreich, R Van der Hofstad - 2017 - Springer
This book focuses on percolation on high-dimensional lattices. We give a general
introduction to percolation, stating the main results and defining the central objects. We …
introduction to percolation, stating the main results and defining the central objects. We …
[ספר][B] Random walks on disordered media and their scaling limits
T Kumagai - 2014 - Springer
The main theme of these lecture notes is to analyze heat conduction on disordered media
such as fractals and percolation clusters by means of both probabilistic and analytic …
such as fractals and percolation clusters by means of both probabilistic and analytic …
The Alexander-Orbach conjecture holds in high dimensions
We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-
field behavior has been established, namely when the dimension d is large enough or when …
field behavior has been established, namely when the dimension d is large enough or when …
Random subgraphs of finite graphs: I. The scaling window under the triangle condition
We study random subgraphs of an arbitrary finite connected transitive graph 𝔾 obtained by
independently deleting edges with probability 1− p. Let V be the number of vertices in 𝔾, and …
independently deleting edges with probability 1− p. Let V be the number of vertices in 𝔾, and …
Phase transitions on nonamenable graphs
arxiv:math/9908177v3 [math.PR] 16 Jun 2000 Page 1 arxiv:math/9908177v3 [math.PR] 16 Jun
2000 J. Math. Phys. 41 (2000), 1099–1126. Version of 30 March 2000 Phase Transitions on …
2000 J. Math. Phys. 41 (2000), 1099–1126. Version of 30 March 2000 Phase Transitions on …
Arm exponents in high dimensional percolation
We study the probability that the origin is connected to the sphere of radius $ r $(an arm
event) in critical percolation in high dimensions, namely when the dimension $ d $ is large …
event) in critical percolation in high dimensions, namely when the dimension $ d $ is large …
The random-cluster model
The class of random-cluster models is a unification of a variety of stochastic processes of
significance for probability and statistical physics, including percolation, Ising, and Potts …
significance for probability and statistical physics, including percolation, Ising, and Potts …
Gibbs measures on Cayley trees: results and open problems
The purpose of this review paper is to present systematically all known results on Gibbs
measures on Cayley trees (Bethe lattices). There are about 150 papers which contain …
measures on Cayley trees (Bethe lattices). There are about 150 papers which contain …
Random Subgraphs Of Finite Graphs: III. The Phase Transition For The n-Cube
We study random subgraphs of the n-cube 0, 1 n, where nearest-neighbor edges are
occupied with probability p. Let pc (n) be the value of p for which the expected size of the …
occupied with probability p. Let pc (n) be the value of p for which the expected size of the …