Probability theory is based on the notion of independence. The celebrated law of large numbers and the central limit theorem describe the asymptotics of the sum of independent variables. However, there are many models of strongly correlated random variables: for instance, the ei…
Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. This book offers beginners a fairly balanced collection of basic facts and methods.
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 deviation theory with basic statistical mechanics, namely Gibbs measures with their variational characterization and th…
Large deviations and thermodynamical formalism: The almost Borel structure of diffeomorphisms with some hyperbolicity / Jérôme Buzzi. Lectures on large deviations in probability and dynamical systems / Yuri Kifer. Thermodynamic formalism for countable Markov shifts / Omri M. Sar…
This volume contains the proceedings of the semester-long special program on Hyperbolic Dynamics, Large Deviations and Fluctuations, which was held from January-June 2013, at the Centre Interfacultaire Bernoulli, École Polytechnique Fédérale de Lausanne, Switzerland. The broad t…
