**CRM Monograph Series**

Volume: 25;
2005;
133 pp;
Hardcover

MSC: Primary 60;
Secondary 62; 76; 82; 86; 94

**Print ISBN: 978-0-8218-3843-3
Product Code: CRMM/25**

List Price: $46.00

Individual Member Price: $36.80

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# Information Theory and Stochastics for Multiscale Nonlinear Systems

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*Andrew J. Majda; Rafail V. Abramov; Marcus J. Grote*

A co-publication of the AMS and Centre de Recherches Mathématiques

This book introduces mathematicians to the fascinating mathematical interplay between ideas from stochastics and information theory and practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena.

After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of complex nonlinear systems. After a general discussion, a new elementary model, motivated by issues in climate dynamics, is utilized to develop a self-contained example of stochastic mode reduction.

Based on A. Majda's Aisenstadt lectures at the University of Montreal, the book is appropriate for both pure and applied mathematics graduate students, postdocs and faculty, as well as interested researchers in other scientific disciplines. No background in geophysical flows is required.

*Andrew Majda* is a member of the
National Academy of Sciences and has received numerous honors and
awards, including the National Academy of Science Prize in Applied
Mathematics, the John von Neumann Prize of the Society of Industrial
and Applied Mathematics, the Gibbs Prize of the American Mathematical
Society, and the Medal of the College de France. In the past several
years at the Courant Institute, Majda and a multi-disciplinary faculty
have created the Center for Atmosphere Ocean Science to promote
cross-disciplinary research with modern applied mathematics in climate
modeling and prediction. *R.V. Abramov* is a young researcher; he
received his PhD in 2002. *M. J. Grote* received his Ph.D. under Joseph
B. Keller at Stanford University in 1995.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Table of Contents

# Table of Contents

## Information Theory and Stochastics for Multiscale Nonlinear Systems

#### Readership

Graduate students and research mathematicians interested in multiscale modeling, information theory, and geophysical flows.