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Stochastic Analysis: The Continuum random tree II: an overview
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.
Lower bounds for covering times for reversible Markov chains and random walks on graphs
For simple random walk on aN-vertex graph, the mean time to cover all vertices is at leastcN log(N), wherec>0 is an absolute constant. This is deduced from a more general result about stationary
Stopping Times and Tightness. II
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
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-transitive graphs.
Probability Approximations via the Poisson Clumping Heuristic
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
Brownian excursions, critical random graphs and the multiplicative coalescent
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
By analogy with the theory surrounding the Ewens sampling formula in neutral population genetics, we ask whether there exists a natural one-parameter family of probability distributions on cladograms