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On the singularity probability of random Bernoulli matrices

Combinatorics 2008-08-06 v2

Abstract

Let nn be a large integer and MnM_n be a random nn by nn matrix whose entries are i.i.d. Bernoulli random variables (each entry is ±1\pm 1 with probability 1/2). We show that the probability that MnM_n is singular is at most (3/4+o(1))n(3/4 +o(1))^n, improving an earlier estimate of Kahn, Koml\'os and Szemer\'edi, as well as earlier work by the authors. The key new ingredient is the applications of Freiman type inverse theorems and other tools from additive combinatorics.

Keywords

Cite

@article{arxiv.math/0501313,
  title  = {On the singularity probability of random Bernoulli matrices},
  author = {Terence Tao and Van Vu},
  journal= {arXiv preprint arXiv:math/0501313},
  year   = {2008}
}

Comments

30 pages, no figures. This is the final version