On permanents of random matrices with positive elements

Details On permanents of random matrices with positive elements On permanents of random matrices with positive elements

2011-11-15

arxiv.org/abs/1111.3454v1

Mathematics

Probability

18 pages, no figures

Scientific paper

We study the asymptotic behavior of permanents of nxn random matrices A with independent identically distributed positive entries and prove a strong law of large numbers for log per A. We calculate the values of the limit lim_n (log per A)/(n \log n) under the assumption that elements have power law decaying tails, and observe a first order phase transition in the limit as the mean becomes infinite. The methods extend to a wide class of rectangular matrices. It is also shown that in finite mean regime the limiting behavior holds uniformly over all submatrices of linear size.

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