论文信息 - Concentration of permanent estimators for certain large matrices

Concentration of permanent estimators for certain large matrices

Let An = (aij) n=1 be an n n positive matrix with entries in [a;b]; 0 < a b. Let Xn = ( p aijxij) n=1 be a random matrix wherefxijg are i.i.d. N(0; 1) random variables. We show that for large n, det(X T n Xn) concentrates sharply at the permanent of An, in the sense that n 1 log(det(X T n Xn)=per An)!n!1 0 in probability.

Shmuel Friedland | Ofer Zeitouni | Brian Rider

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