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

✍ Scribed by Frank Spitzer (auth.), Rick Durrett, Harry Kesten (eds.)

• Publisher: Birkhäuser Basel
• Year: 1991
• Tongue: English
• Leaves: 471
• Series: Progress in Probability 28
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Front Matter....Pages 1-1
A Combinatorial Lemma and its Application to Probability Theory....Pages 3-19
Some Theorems Concerning 2-Dimensional Brownian Motion....Pages 21-31
Recurrent Random Walk and Logarithmic Potential....Pages 33-52
Electrostatic Capacity, Heat Flow, and Brownian Motion....Pages 53-65
Interaction of Markov Processes....Pages 66-110
Front Matter....Pages 111-111
A Useful Renormalization Argument....Pages 113-152
Capture Problems For Coupled Random Walks....Pages 153-188
Nonlinear Voter Models....Pages 189-201
On the Long Term Behavior of Finite Particle Systems: A Critical Dimension Example....Pages 203-213
Large Deviation Lower Bounds For General Sequences Of Random Variables....Pages 215-221
Asymptotic Laplace-Transforms....Pages 223-230
Higher Order Hydrodynamic Equations for a System of Independent Random Walks....Pages 231-254
Making Money From Fair Games....Pages 255-267
Additive Functionals of Superdiffusion Processes....Pages 269-281
Interacting Systems, Stirrings, and Flows....Pages 283-293
The One Dimensional Stochastic X-Y Model....Pages 295-307
Relations Between Solutions to a Discrete and Continuous Dirichlet Problem....Pages 309-321
On the Connected Components of the Complement of a Two-Dimensional Brownian Path....Pages 323-338
The Periodic Threshold Contact Process....Pages 339-358
Bounds on the Critical Exponent of Self-Avoiding Polygons....Pages 359-371
Front Matter....Pages 111-111
Spitzer’s Formula Involving Capacity....Pages 373-388
An Integral Test for Subordinators....Pages 389-398
Microcanonical Distributions, Gibbs States, and the Equivalence of Ensembles....Pages 399-424
Power Counting Theorem in Euclidean Space....Pages 425-440
Etude asymptotique des nombres de tours de plusieurs mouvements browniens complexes corrélés....Pages 441-455
Back Matter....Pages 457-458

✦ Subjects

Probability Theory and Stochastic Processes