Random matrices: tail bounds for gaps between eigenvalues

By Hoi H. Nguyen, Terence Tao, Van H. Vu. Probability theory and related fields, 2015

73 citations recorded by the source corpus.

Gaps (or spacings) between consecutive eigenvalues are a central topic in random matrix theory. The goal of this paper is to study the tail distribution of these gaps in various random matrix models. We give the first repulsion bound for random matrices with discrete entries and the first super-polynomial bound on the probability that a random graph has simple spectrum, along with several applications.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/54fd32bf0f418b47eba81da7c086aee6f8ca332c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Roman Vershynin
2. Mark Rudelson
3. Konstantin E. Tikhomirov
4. Van H. Vu
5. Jaouad Mourtada
6. Terence Tao
7. Hoi H. Nguyen
8. Nicholas A. Cook

In Mathematical Physics

1. Roman Vershynin
2. Mark Rudelson
3. Konstantin E. Tikhomirov
4. Van H. Vu
5. Nicholas A. Cook
6. Terence Tao
7. Hoi H. Nguyen
8. E.J. Candes

In Statistics and Probability

1. Roman Vershynin
2. Mark Rudelson
3. Konstantin E. Tikhomirov
4. Van H. Vu
5. Nicholas A. Cook
6. Terence Tao
7. Jaouad Mourtada
8. Hoi H. Nguyen

Citations in the corpus

• No-gaps delocalization for general random matrices (2015, background): “Proof of Theorem 6.1 on invertibility for general distributions 41 References 44”