On random ±1 matrices: Singularity and determinant

  • Authors:

  • Terence Tao;Van Vu

  • Affiliations:

  • Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90095-1555;Department of Mathematics, University of California at San Diego, La Jolla, California, 92093-0112

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 2006

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Abstract

This papers contains two results concerning random n × n Bernoulli matrices. First, we show that with probability tending to 1 the determinant has absolute value $\sqrt{n!}\exp(O(\sqrt{n \ln n}))$. Next, we prove a new upper bound 0.958n on the probability that the matrix is singular.© 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006