A simple observation on random matrices with continuous diagonal entries

作者：Friedland Omer^*; Giladi Ohad

来源：Electronic Communications in Probability, 2013, 18(none): 1-7.

DOI：10.1214/ECP.v18-2633

• Random matrices
• Singular values
• Small ball probability
• Determinant

Let T be an n x n random matrix, such that each diagonal entry T-i,T-i is a continuous random variable, independent from all the other entries of T. Then for every n x n matrix A and every t >= 0
P[vertical bar det(A + T)vertical bar(1/n) <= t] <= 2bnt,
where b > 0 is a uniform upper bound on the densities of T-i,T-i.

• 出版日期2013-6-30