2026-07-23T06:18:23Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14726 2024-03-06T10:54:45Z ddc:004 open_access

Singularity of Random Integer Matrices with Large Entries Karingula, Sankeerth Rao Lovett, Shachar Coding Theory Random matrix theory Singularity probability MDS codes Error correction codes Littlewood Offord Fourier Analysis We study the singularity probability of random integer matrices. Concretely, the probability that a random n × n matrix, with integer entries chosen uniformly from {-m,…,m}, is singular. This problem has been well studied in two regimes: large n and constant m; or large m and constant n. In this paper, we extend previous techniques to handle the regime where both n,m are large. We show that the probability that such a matrix is singular is m^{-cn} for some absolute constant c > 0. We also provide some connections of our result to coding theory. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sankeerth Rao Karingula and Shachar Lovett 2021 Is Part Of LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2021.33 urn:nbn:de:0030-drops-147260 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.33 eng https://creativecommons.org/licenses/by/4.0/legalcode