Work

Some new results in random matrices over finite fields

Year: 2020

Type: article

Abstract: In this note, we give various characterizations of random walks with possibly different steps that have relatively large discrepancy from the uniform distribution modulo a prime p, and use these results to study the distribution of the rank of random matrices over F p and the equi-distribution behavior of normal vectors of random hyperplanes. We also study the probability that a random square matrix is eigenvalue-free, or when its characteristic polynomial is divisible by a given irreducible polynomial in the limit n → ∞ in F p . We show that these statistics are universal, extending results of Stong and Neumann-Praeger beyond the uniform model.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.12405

Authors: Kyle Luh, Sean Meehan, Hoi H. Nguyen

Institutions: University of Colorado Boulder, University of Colorado System, The Ohio State University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Singularity, Universality, and Smoothness of Random Walks, PostDoctoral Research Fellowship