Random Matrices, Frobenius Eigenvalues, and Monodromy
Will be published approx. on 13. November 1999
Book
Paperback/Softback
419 pages
978-1-4704-7507-9 (ISBN)
Description
The main topic of this book is the deep relation between the spacings between zeros of zeta and $L$-functions and spacings between eigenvalues of random elements of large compact classical groups. The authors draw upon many disparate areas of mathematics from algebraic geometry, moduli spaces, mondromy, equidistribution, and the Weil conjectures to probability theory and the compact classical groups.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
ISBN-13
978-1-4704-7507-9 (9781470475079)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Nicholas M. Katz, Princeton University, NJ.
Peter Sarnak, Princeton University, NJ
Peter Sarnak, Princeton University, NJ
Content
Statements of the main results
Reformulation of the main results
Reduction steps in proving the main theorems
Test functions
Haar measure
Tail estimates
Large $N$ limits and Fredholm determinants
Several variables
Equidistribution
Monodromy of families of curves
Monodromy of some other families
GUE discrepancies in various families
Distribution of low-lying Frobenius eigenvalues in various families
Appendix AD: Densities
Appendix AG: Graphs
References.
Reformulation of the main results
Reduction steps in proving the main theorems
Test functions
Haar measure
Tail estimates
Large $N$ limits and Fredholm determinants
Several variables
Equidistribution
Monodromy of families of curves
Monodromy of some other families
GUE discrepancies in various families
Distribution of low-lying Frobenius eigenvalues in various families
Appendix AD: Densities
Appendix AG: Graphs
References.