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Random walk intersections. Large deviations and related topics. (English) Zbl 1192.60002
Mathematical Surveys and Monographs 157. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4820-3/hbk). x, 332 p. (2009).
The book displays recent results on large deviations occurring in sample path intersections, and more especially it deals with the probability that random walks and Brownian motions intersect each other with large intensity. Brownian intersection, mutual intersection, self-intersection and intersections on lattices are successively considered, and then one focuses on large deviations in independent random walks on the one hand, and single random walk on the other hand. The mathematics is classical, and reading the book requires only the basics of stochastic processes and of functional analysis. Each chapter is closed with a set of problems for solution, what is very interesting from the pedagogical standpoint.

60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60F05 Central limit and other weak theorems
60F10 Large deviations
60F15 Strong limit theorems
60F25 \(L^p\)-limit theorems
60G17 Sample path properties
81T17 Renormalization group methods applied to problems in quantum field theory
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)