Invertibility of random fredholm operators

Abstract

Given a Gaussian measure μ on the space K(X) of compact operators on a Banach space X, we study the distribution of the norm of the inverse of the random Fredholm operator I_X+T, that is where I_X is the identity on X. For random integral operators T distributed according to a Wiener type measure on the space of kernels we obtain almost sharp two–sided estimates of F(t). The methods yield also some new estimates of average condition numbers of random matrices.