Abstract
Dedicated to Professor K. R. Parthasarathy on the occasion of his 75th birthday Abstract. We prove a large deviation result for a random symmetric n n matrix with independent identically distributed entries to have a few eigen- values of size n. If the spectrum S survives when the matrix is rescaled by a factor of n, it can only be the eigenvalues of a Hilbert-Schmidt kernel k(x;y) on (0;1) (0;1). The rate function for k is I(k) = 1 R h(k(x; y)dxdy where h is the Cramer rate function for the common distribution of the entries that is assumed to have a tail decaying faster than any Gaussian. The large deviation for S is then obtained by contraction.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
