On the permanent of random Bernoulli matrices

2008/04/15 by Tao, T., Vu, V. · 3 citations
#05D40 #15A15 #15A52 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0804.2362

Abstract

We show that the permanent of an n × n matrix with iid Bernoulli entries ± 1 is of magnitude n^(1/2+o(1))n with probability 1-o(1). In particular, it is almost surely non-zero.

Cited by

• Probabilistic combinatorics at exponentially small scales
• Permanental rank versus determinantal rank of random matrices over finite fields
• Exponential anticoncentration of the permanent

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• Approximating the Permanent of a Random Matrix with Vanishing Mean
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• A general law of large permanent