Random Matrices, Frobenius Eigenvalues, and Monodromy
Heftet /
1999
/ Engelsk
Produktdetaljer
ISBN
9781470475079
Publisert
1999-11-13
Utgiver
American Mathematical Society; American Mathematical Society
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
419
Om bidragsyterne
Nicholas M. Katz, Princeton University, NJ.Peter Sarnak, Princeton University, NJ
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.
Les mer
- 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.
Les mer
Produktdetaljer
ISBN
9781470475079
Publisert
1999-11-13
Utgiver
American Mathematical Society; American Mathematical Society
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
419
Om bidragsyterne
Nicholas M. Katz, Princeton University, NJ.Peter Sarnak, Princeton University, NJ