Random Walks of Infinitely Many Particles

The author's previous book, Random Walk in Random and Non-Random Environments, was devoted to the investigation of the Brownian motion of a simple particle. The present book studies the independent motions of infinitely many particles in the d-dimensional Euclidean space Rd. In Part I the particles at time t = 0 are distributed in Rd according to the law of a given random field and they execute independent random walks. Part II is devoted to branching random walks, i.e. to the case where the particles execute random motions and birth and death processes independently. Finally, in Part III, functional laws of iterated logarithms are proved for the cases of independent motions and branching processes. Contents:Random Walk of a Random Field:Brownian Motion of a Poisson FieldExtreme Value ProblemsChanging the Initial Process and the MotionBranching Random Walk:Branching Random Walk Starting with One ParticleBranching Random Walks of a Random FieldBranching Wiener Process Starting with One ParticleCritical Branching Random Walk Starting with One ParticleCritical Branching Random Walks of a Random FieldMultitype Branching Random WalkStrassen Type Theorems:Infinitely Many Independent ParticlesBranching Random Walk Readership: Mathematicians. keywords:Random Field;Poisson Field;Brownian Motion;Brownian Density Process;Extreme Value Problems;Coupling;Branching Process;Branching Random Walk;Strassen Type Theorems