Perplexing problems in probability

For almost four decades Harry Kesten has been known throughout the world as a prodigious problem solver. In the 60s, he proved many refined results on random walks and continuous time processes with stationary independent increments. This research continued in the 70s with impressive contributions to renewal theory and branching processes, but soon Kesten's work moved toward topics inspired by physics: random walks in random environment, diffusions with random coefficients and self-similar processes. The 80s began with his proof that 'the critical probability of percolation on the square lattice equals 1/2,' followed by an explosion of results on percolation and first passage percolation. In the late 80s and into the 90s, he obtained deep results on the behavior of percolation near the critical value, used percolation methods to study the Ising model, and proved remarkable results about diffusion limited aggregation and the sub-diffusive fluctuation in first passage percolation. To this day he continues to work on hard open problems, a number of which come from physics. To honor Kesten's achievements, and to highlight important directions for future research, a number of prominent probabilists have written survey articles on a wide variety of active areas of contemporary probability, many of which are closely related to Kesten's work. This festschrift volume is an expression of appreciation and a demonstration of the depth and breadth of his ideas. Series: Progress in Probability, Vol. 44 Table of Contents Harry Kesten's Publications: A Personal Perspective By Rick Durrett Lattice Trees, Percolation, and Super-Brownian Motion By Gordon Slade Percolation In {infinity}+1 Dimensions at the Uniqueness Threshold By Roberto Schonmann Percolation on Transitive Graphs as a Coalescent Process: Relentless Merging Followed by Simultaneous Uniqueness By Olle Haggstrom, Yuval Peres and Roberto Schonmann Inequalities and Entanglements for Percolation and Random Cluster Models By Goeff Grimmett From Greedy Lattice Animals to First Passage Percolation By Doug Howard and Charles Newman Reverse Shapes in First Passage Percolation and Related Growth Models By Janko Gravner and David Griffeath Double Behaviors of Critical First Passage Percolation By Yu Zhang The Van Den Berg-Kesten-Reimer Inequality: A Review By Christian Borgs, Jennifer Chayes, and Dana Randall Large Scale Degrees and the Number of Spanning Clusters for the Uniform Spanning Tree By Itai Benjamini On the Absence of Phase Transition in the Monomer-Dimer Model By J. van den Berg Loop Erased Random Walk By Greg Lawler Dominance of the Sum over the Maximum and Some New Classes of Stochastic Compactness By Phil Griffin and Ross Maller Stability and Heavy Traffic Limits for Queuing Networks By Maury Bramson Rescaled Particle Systems Converging to Super-Brownian Motion By Ted Cox, Rick Durrett and Ed Perkins The Hausdorff Measure of the Range of Super-Brownian Motion By Jean-Francois Le Gall Branching Random Walks on Finite Trees By Tom Liggett Toom's Stability Theorem in Continuous Time By Larry Gray The Role of Explicit Space in Plant Competition Models By Claudia Neuhauser Large Derivations for the Simple Exclusion Process By Srinivasa Varadhan The Gibbs Conditioning Principle for Markov Chains By Ana Meda and Peter Ney