Random Walks, Brownian Motion, and Interacting Particle Systems: A Festschrift in Honor of Frank Spitzer

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H. Kesten, R. Durrett
Springer Science & Business Media, Jun 1, 1991 - Mathematics - 455 pages
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.
 

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Contents

A combinational lemma and its application to probability theory
323
Some theorems concerning 2dimensional Brownian motion
201
Recurrent random walk and logarithmic potential
213
Electrostatic capacity heat flow and Brownian motion
233
Interaction of Markov processes
246
Papers Dedicated to Frank Spitzer
111
A Useful Renormalization Argument
113
Capture Problems for Coupled Random Walks
153
Additive Functionals of Superdiffusion Processes
269
Interacting Systems Stirrings and Flows
283
The OneDimensional Stochastic XY Model
295
Relations Between Solutions to a Discrete and Continuous Dirichlet Problem
309
On the Connected Components of the Complement of a TwoDimensional Brownian Path
323
The periodic Threshold Contact Process
339
Bounds on the Critical Exponent of SelfAvoiding Polygons
359
Spitzers Formula Involving Capacity
373

Nonlinear Voter Models
189
On the Long Term Behavior of Finite Particle Systems A Critical Dimension Example
203
Large Deviation Lower Bounds for General Sequences of Random Variables
215
Asymptotic LaplaceTransforms
223
Higher Order Hydrodynamic Equations for a System of Independent Random Walks
231
Making Money From Fair Games
255
An Integral Test for Subordinators
389
Microcanonical Distributions Gibbs States and the Equivalence of Ensembles
399
Power Counting Theorem in Euclidean Space
425
Etude asymptotique des nombres de tours de plusieurs mouvements browniens complexes corrélés
441
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