This is an introductory course on the methods of computing asymptotics of probabilities of rare events: the theory of large deviations. The book combines large

This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable r

The aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure

This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classi

This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate cours