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Hitting Time Theorems for Random Matrices

Published online by Cambridge University Press:  09 July 2014

LOUIGI ADDARIO-BERRY  and
LAURA ESLAVA
LOUIGI ADDARIO-BERRY
Affiliation:
Department of Mathematics and Statistics, McGill University (e-mail: louigi@math.mcgill.ca, laura.eslavafernandez@mail.mcgill.ca)
LAURA ESLAVA
Affiliation:
Department of Mathematics and Statistics, McGill University (e-mail: louigi@math.mcgill.ca, laura.eslavafernandez@mail.mcgill.ca)
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Abstract

Starting from an n-by-n matrix of zeros, choose uniformly random zero entries and change them to ones, one at a time, until the matrix becomes invertible. We show that with probability tending to one as n → ∞, this occurs at the very moment the last zero row or zero column disappears. We prove a related result for random symmetric Bernoulli matrices, and give quantitative bounds for some related problems. These results extend earlier work by Costello and Vu [10].

Keywords

Primary 15A52Secondary 15A1505C80

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 5: Honouring the Memory of Philippe Flajolet - Part 1 , September 2014 , pp. 635 - 669
Copyright
Copyright © Cambridge University Press 2014 

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