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Markov Chains and Mixing Times
This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationaryExpand
Determinantal Processes and Independence
We give a probabilistic introduction to determinantal and per- manental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatoricsExpand
Probability on Trees and Networks
Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties togetherExpand
Zeros of Gaussian Analytic Functions and Determinantal Point Processes
The book examines in some depth two important classes of point processes, determinantal processes and 'Gaussian zeros', i.e., zeros of random analytic functions with Gaussian coefficients, which share a property of 'point-repulsion', and presents a primer on modern techniques on the interface of probability and analysis. Expand
Conceptual proofs of L log L criteria for mean behavior of branching processes
The Kesten-Stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an L log L condition is decisive. In critical and subcritical cases,Expand
Tug-of-war and the infinity Laplacian
We consider a class of zero-sum two-player stochastic games called tug-of-war and use them to prove that every bounded real-valued Lipschitz function F on a subset Y of a length space X admits aExpand
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 (FSF) or wired (WSF)Expand
Broadcasting on trees and the Ising model
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology andExpand
Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions
Erdős (1939, 1940) studied the distribution νλ of the random series P∞ 0 ±λn, and showed that νλ is singular for infinitely many λ ∈ (1/2, 1), and absolutely continuous for a.e. λ in a small intervalExpand
Group-invariant Percolation on Graphs
Abstract. Let G be a closed group of automorphisms of a graph X. We relate geometric properties of G and X, such as amenability and unimodularity, to properties of G-invariant percolation processesExpand