Random Matrices, Frobenius Eigenvalues, and Monodromy

Nicholas M. Katz, Peter Sarnak

Type: Book

Publication Date: 1998-11-24

Citations: 708

DOI: https://doi.org/10.1090/coll/045

Abstract

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.

Locations

Colloquium Publications - American Mathematical Society/Colloquium Publications - View
Colloquium Publications - American Mathematical Society/Colloquium Publications - View

Similar Works

Action	Title	Year	Authors
+ PDF	Density of Eigenvalues of Random Normal Matrices	2005	Peter Elbau Giovanni Felder
+ PDF Chat	Random matrices: tail bounds for gaps between eigenvalues	2016	Hoi H. Nguyen Terence Tao Van Vu
+ PDF Chat	A Note on the Eigenvalue Density of Random Matrices	1999	Michael K.‐H. Kiessling Herbert Spohn
+ PDF	Eigenvalues of Random Symmetric Matrices	2007
+ PDF	Eigenvalues of Random Symmetric Matrices	2007
+	Eigenvalue correlations for random matrices	1993	Taro Nagao
+	The statistics of the eigenvalues of random matrices	1966	F. Cristofori P.G. Sona F. Tonolini
+	On the density of Eigenvalues of a random matrix	1960	M. L. Mehta M. Gaudin
+	ON THE DENSITY OF EIGENVALUES OF A RANDOM MATRIX	1996	M. L. Mehta M. Gaudin
+	Eigenvalue distribution of random operators and matrices	1992	L. А. Pastur
+	The eigenvalues of random symmetric matrices	1981	Zoltán Füredi János Komlós
+	Distribution of Eigenvalues and Eigenvectors of Random Matrices	1990	Vyacheslav L. Girko
+	ASYMPTOTIC DISTRIBUTION OF EIGENVALUES OF RANDOM MATRICES	1972	W. H. Olson V. R. R. Uppuluri
+ PDF	Asymptotic Distribution of Eigenvalues of Random Matrices	1972	W. H. Olson V. R. R. Uppuluri
+	The Eigenvalues of Random Matrices	2021	Elizabeth Meckes
+	Limit behavior of the spectrum in a class of large random matrices	1997	A Yu Plakhov
+	Limit laws for Random matrices and free products	1991	Dan Voiculescu
+	ASYMPTOTIC DISTRIBUTION OF EIGENVALUES OF RANDOM MATRICES.	1970	W. H. Olson V. R. R. Uppuluri
+	Random matrices and asymptotic freeness	1992	Dan Voiculescu Kenneth J. Dykema Alexandru Nica
+	Large random matrices: Eigenvalue distribution	1993	Benoît Eynard

Works That Cite This (702)

Action	Title	Year	Authors
+	Average rank in families of quadratic twists: a geometric point of view	2015	Pierre Le Boudec
+ PDF Chat	Rigid local systems and alternating groups	2018	Robert M. Guralnick Nicholas M. Katz Pham Huu Tiep
+	Quantitative sheaf theory	2022	Will Sawin Arthur Forey Javier Fresán Emmanuel Kowalski
+	The Ratios Conjecture and upper bounds for negative moments of 𝐿-functions over function fields	2023	Hung M. Bui Alexandra Florea Jonathan P. Keating
+ PDF Chat	A representation theory approach to integral moments of L-functions over function fields	2020	Will Sawin
+ PDF Chat	Bounds for moments of cubic and quartic Dirichlet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e20" altimg="si7.svg"><mml:mi>L</mml:mi></mml:math>-functions	2022	Peng Gao Liangyi Zhao
+	An elliptic curve test of the L-Functions Ratios Conjecture	2011	Duc Khiem Huynh Steven J. Miller Ralph Morrison
+ PDF Chat	The Hilbert series of U/SU SQCD and Toeplitz determinants	2011	Yang Chen Noppadol Mekareeya
+	Low-lying zeros of cubic Dirichlet L-functions and the Ratios conjecture	2019	Peter J. Cho Jeong-Ho Park
+ PDF	Sato-Tate distributions	2019	Andrew V. Sutherland

Works Cited by This (0)

Action	Title	Year	Authors