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Discrete Math

The probability that a matrix with Rademacher entries is normal

Andrei Deneanu, Yale

Location:  Hill 705
Date & time: Monday, 11 February 2019 at 2:00PM - 3:00PM

 
Abstract: We consider a random nxn matrix, M_n, whose entries are independent and identically distributed (i.i.d.) Rademacher random variables (taking values {-1,1} with probability 1/2) and prove 2^{-(0.5+o(1))n^2} <=P (M_n is normal) <= 2^{-(0.302+o(1))n^{2}}.
We conjecture that the lower bound is sharp.