by Pál Révész (Tech. Univ. of Vienna)

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 R^d. In Part I the particles at time t = 0 are distributed in R^d 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.

• Random Walk of a Random Field:
  • Brownian Motion of a Poisson Field
  • Extreme Value Problems
  • Changing the Initial Process and the Motion
• Branching Random Walk:
  • Branching Random Walk Starting with One Particle
  • Branching Random Walks of a Random Field
  • Branching Wiener Process Starting with One Particle
  • Critical Branching Random Walk Starting with One Particle
  • Critical Branching Random Walks of a Random Field
  • Multitype Branching Random Walk
• Strassen Type Theorems:
  • Infinitely Many Independent Particles
  • Branching Random Walk