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Author:   Anne Broise-Alamichel ,  Jouni Parkkonen ,  Frédéric Paulin
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   1st ed. 2019
Volume:   329
Weight:   0.799kg
ISBN:  

9783030183141

ISBN 10:   3030183149
Pages:   413
Publication Date:   02 January 2020
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Introduction.- Negatively curved geometry.- Potentials, critical exponents and Gibbs cocycles.- Patterson-Sullivan and Bowen-Margulis measures with potential on CAT(-1) spaces.- Symbolic dynamics of geodesic flows on trees.- Random walks on weighted graphs of groups.- Skinning measures with potential on CAT(-1) spaces.- Explicit measure computations for simplicial trees and graphs of groups.- Rate of mixing for the geodesic flow.- Equidistribution of equidistant level sets to Gibbs measures.- Equidistribution of common perpendicular arcs.- Equidistribution and counting of common perpendiculars in quotient spaces.- Geometric applications.- Fields with discrete valuations.- Bruhat-Tits trees and modular groups.- Rational point equidistribution and counting in completed function fields.- Equidistribution and counting of quadratic irrational points in non-Archimedean local fields.- Counting and equidistribution of crossratios.- Counting and equidistribution of integral representations by quadratic norm forms.- A - A weak Gibbs measure is the unique equilibrium, by J. Buzzi.- List of Symbols.- Index.- Bibliography.

Reviews

The work under review is a beautiful and very thorough exploration ... . The theorems are stated in great generality, and whenever possible, with explicit error terms in asymptotics of counting/equidistribution, which is very useful in applications. (Jayadev S. Athreya, Mathematical Reviews, April, 2021)

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