1 INTRODUCTION Many different models of random trees have arisen in a variety of applied setting, and there is a large but scattered literature on exact and asymptotic results for particular models.… Expand

A The Heuristic.- B Markov Chain Hitting Times.- C Extremes of Stationary Processes.- D Extremes of Locally Brownian Processes.- E Simple Combinatorics.- F Combinatorics for Processes.- G Exponential… Expand

To establish weak convergence of a sequence of martingales to a continuous martingale limit, it is sufficient (under the natural uniform integrability condition) to establish convergence of… Expand

Consider an array of random variables (Xi,j), 1 ≤ i,j < ∞, such that permutations of rows or of columns do not alter the distribution of the array. We show that such an array may be represented as… Expand

We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs.… Expand

Let (B t (s), 0 ≤ s < ∞) be reflecting inhomogeneous Brownian motion with drift t - s at time s, started with B t (0) = 0. Consider the random graph script G sign(n, n -1 + tn -4/3 ), whose largest… Expand