The material covered in this book involves important and non-trivial results in contemporary probability theory motivated by polymer models, as well as other topics of importance in physics and chemistry. The development carefully provides the basic definitions of mutual intersection and self-intersection local times for Brownian motions and the accompanying large deviation results. The book then proceeds to the analogues of these concepts and results for random walks on lattices of $R^d$. This includes suitable integrability and large deviation results for these models and some applications. Moreover, the notes and comments at the end of the chapters provide interesting remarks and references to various related results, as well as a good number of exercises. The author provides a beautiful development of these subtle topics at a level accessible to advanced graduate students.

Readership

Graduate students and research mathematicians interested in probability and statistical physics.

Table of Contents

• Basics on large deviations
• Brownian intersection local times
• Mutual intersection: large deviations
• Self-intersection: large deviations
• Intersections on lattices: weak convergence
• Inequalities and integrabilities
• Independent random walks: large deviations
• Single random walk: large deviations
• Green's function
• Fourier transformation
• Constant $\kappa(d,p)$ and related variations
• Regularity of stochastic processes
• Self-adjoint operators
• Bibliography
• List of general notations
• Index