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On random ±1 matrices: Singularity and determinant
Author(s) -
Tao Terence,
Vu Van
Publication year - 2006
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20109
Subject(s) - mathematics , bernoulli's principle , random matrix , struct , combinatorics , singular value , upper and lower bounds , matrix (chemical analysis) , singularity , value (mathematics) , expected value , discrete mathematics , physics , statistics , mathematical analysis , computer science , quantum mechanics , eigenvalues and eigenvectors , materials science , composite material , thermodynamics , programming language
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 0.958 n on the probability that the matrix is singular.© 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006