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Hyperbolic Dynamics and Brownian Motion
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Hyperbolic Dynamics and Brownian Motion: An Introduction

Jacques Franchi and Yves Le Jan

Abstract

The idea of this book is to illustrate an interplay between distinct domains of mathematics. Firstly, this book provides an introduction to hyperbolic geometry, based on the Lorentz group PSO(1, d) and its Iwasawa decomposition, commutation relations and Haar measure, and on the hyperbolic Laplacian. The Lorentz group plays a role in relativistic space–time analogous to rotations in Euclidean space. Hyperbolic geometry is the geometry of the unit pseudo-sphere. The boundary of hyperbolic space is defined as the set of light rays. Special attention is given to the geodesic and horocyclic flows. ... More

Keywords: Lorentz–Möbius group, Minkowski space, hyperbolic geometry, geodesic flow, Haar measure, hyperbolic Laplacian, Kleinian groups, Poincaré inequality, group-valued Brownian motions, relativistic diffusion, Sinai central limit theorem

Bibliographic Information

Print publication date: 2012 Print ISBN-13: 9780199654109
Published to Oxford Scholarship Online: January 2013 DOI:10.1093/acprof:oso/9780199654109.001.0001

Authors

Affiliations are at time of print publication.

Jacques Franchi, author
Professor of Mathematics, Université de Strasbourg

Yves Le Jan, author
Professor of Mathematics, Université Paris Sud (Orsay) and Institut Universitaire de France

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