Invertibility of random fredholm operators
- 1 January 1990
- journal article
- research article
- Published by Taylor & Francis in Stochastic Analysis and Applications
- Vol. 8 (1) , 1-59
- https://doi.org/10.1080/07362999008809197
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 IX+T, that is where IX 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.Keywords
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