Recurrence of distributional limits of finite planar graphs
I Benjamini, O Schramm - Selected Works of Oded Schramm, 2011 - Springer
Suppose that G j is a sequence of finite connected planar graphs, and in each G ja special
vertex, called the root, is chosen randomly-uniformly. We introduce the notion of a …
vertex, called the root, is chosen randomly-uniformly. We introduce the notion of a …
Processes on unimodular random networks
We investigate unimodular random networks. Our motivations include their characterization
via reversibility of an associated random walk and their similarities to unimodular quasi …
via reversibility of an associated random walk and their similarities to unimodular quasi …
[BOOK][B] Topics in orbit equivalence
A Kechris, BD Miller - 2004 - books.google.com
This volume provides a self-contained introduction to some topics in orbit equivalence
theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and …
theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and …
Phase transitions on nonamenable graphs
R Lyons - Journal of Mathematical Physics, 2000 - pubs.aip.org
We shall give a summary of some of the main results known about phase transitions on
nonamenable graphs. All terms will be defined as needed beginning in Sec. II. Among the …
nonamenable graphs. All terms will be defined as needed beginning in Sec. II. Among the …
Determinantal probability measures
R Lyons - Publications Mathématiques de l'IHÉS, 2003 - numdam.org
Determinantal point processes have arisen in diverse settings in recent years and have
been investigated intensively. We study basic combinatorial and probabilistic aspects in the …
been investigated intensively. We study basic combinatorial and probabilistic aspects in the …
On the growth of -invariants for sequences of lattices in Lie groups
We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral
invariants of sequences of locally symmetric spaces. Our main results are uniform versions …
invariants of sequences of locally symmetric spaces. Our main results are uniform versions …
Special invited paper: uniform spanning forests
We study uniform spanning forest measures on infinite graphs, which are weak limits of
uniform spanning tree measures from finite subgraphs. These limits can be taken with free …
uniform spanning tree measures from finite subgraphs. These limits can be taken with free …
[BOOK][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 …
Asymptotic enumeration of spanning trees
R Lyons - Combinatorics, Probability and Computing, 2005 - cambridge.org
We give new formulas for the asymptotics of the number of spanning trees of a large graph.
A special case answers a question of McKay [Europ. J. Combin. 4 149–160] for regular …
A special case answers a question of McKay [Europ. J. Combin. 4 149–160] for regular …
The random geometry of equilibrium phases
Publisher Summary This chapter discusses the random geometry of equilibrium phases.
Percolation will come into play here on various levels. Its concepts like clusters, open paths …
Percolation will come into play here on various levels. Its concepts like clusters, open paths …