Random Walks, Brownian Motion, and Interacting Particle Systems

This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come. Frank has always liked new phenomena, clean formulations and elegant proofs. He has created or opened up several research areas and it is not surprising that many people are still working out the consequences of his inventions. By way of introduction we have reprinted some of Frank's seminal articles so that the reader can easily see for himself the point of origin for much of the research presented here. These articles of Frank's deal with properties of Brownian motion, fluctuation theory and potential theory for random walks, and, of course, interacting particle systems. The last area was started by Frank as part of the general resurgence of treating problems of statistical mechanics with rigorous probabilistic tools.

Reprints of Frank Spitzer. - A combinatorial lemma and its application to probability theory. - Some theorems concerning 2-dimensional Brownian motion. - Recurrent random walk and logarithmic potential. - Electrostatic capacity, heat flow and Brownian motion. - Interaction of Markov processes. - Papers Dedicated to Frank Spitzer. - A Useful Renormalization Argument. - Capture Problems for Coupled Random Walks. - Nonlinear Voter Models. - On the Long Term Behavior of Finite Particle Systems: A Critical Dimensional Example. - Large Deviation Lower Bounds for General Sequences of Random Variables. - Asymptotic Laplace-Transforms. - Higher Order Hydrodynamic Equations for a System of Independent Random Walks. - Making Money From Fair Games. - Additive Functionals of Superdiffusion Processes. - Interacting Systems, Stirrings, and Flows. - The One-Dimensional Stochastic X-Y Model. - Relations Between Solutions to a Discrete and Continuous Dirichlet Problem. - On the Connected Components of the Complement of a Two-Dimensional Brownian Path. - The periodic Threshold Contact Process. - Bounds on the Critical Exponent of Self-Avoiding Polygons. - Spitzer s Formula Involving Capacity. - An Integral Test for Subordinators. - Microcanonical Distribution, Gibbs States, and the Equivalence of Ensembles. - Power Counting Theorem in Euclidean Space. - Etude asymptotique des nombres de tours de plusieurs mouvements browniens complexes corrélés.