Large deviation estimates have proved to be a crucial tool in statistics, engineering, statistical mechanics, and applied probability. This new edition presents an introduction to the theory of large deviations, with rigorous mathematical applications from a wide range of areas, including electrical engineering and DNA sequencing.

Large Deviations Techniques and Applications (Stochastic Modelling and Applied Probability)

Science & Math

Dembo, Amir

Zeitouni, Ofer

Mathematics

Springer

The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence.

An Introduction to Random Matrices (Cambridge Studies in Advanced Mathematics)

Anderson, Greg W.

Guionnet, Alice

Cambridge University Press

The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence.

An Introduction to Random Matrices (Cambridge Studies in Advanced Mathematics, Series Number 118)

Concerned with the study of the probabilities of very rare events yes, like winning the Lottery discussion includes large deviations for finite dimensional spaces, Cramer's theorem, the Gartner-Ellis theorem, applications of the finite dimensional case, Sanov's theorem, finite state Markov chains, the Gibbs conditioning principle, Vasradhan's integral lemma, sample path large deviations, tracking loops, and using large deviation for abstract empirical measures. A glossary of symbols is included. Annotation copyright Book News, Inc. Portland, Or.

Large Deviations Techniques and Applications (Jones and Bartlett Books in Mathematics)

Jones& Bartlett Learning

This book provides an introduction to the theory of large deviations and applications. This softcover edition is a corrected printing of the 1998 edition.

Large Deviations Techniques and Applications (Stochastic Modelling and Applied Probability, 38)

Large Deviations Techniques and Applications

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