License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.33
URN: urn:nbn:de:0030-drops-147260
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14726/
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Karingula, Sankeerth Rao ; Lovett, Shachar

Singularity of Random Integer Matrices with Large Entries

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LIPIcs-APPROX33.pdf (0.7 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{karingula_et_al:LIPIcs.APPROX/RANDOM.2021.33,
  author =	{Karingula, Sankeerth Rao and Lovett, Shachar},
  title =	{{Singularity of Random Integer Matrices with Large Entries}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14726},
  URN =		{urn:nbn:de:0030-drops-147260},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.33},
  annote =	{Keywords: Coding Theory, Random matrix theory, Singularity probability MDS codes, Error correction codes, Littlewood Offord, Fourier Analysis}
}

Keywords: Coding Theory, Random matrix theory, Singularity probability MDS codes, Error correction codes, Littlewood Offord, Fourier Analysis
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)
Issue Date: 2021
Date of publication: 15.09.2021

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