Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 159, Issue 6, Pages 1306-1326Publisher
SPRINGER
DOI: 10.1007/s10955-015-1228-7
Keywords
Large deviations; Replica method; Random matrices; Spin glass
Categories
Funding
- NSF [DMS-1106627]
- Israel Science Foundation
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We consider the quadratic optimization problem Fnw,h := sup(x is an element of/Sn-1) (1/2x(t) Wx + h(T)x), with a (random) matrix and a random external field. We study the probabilities of large deviation of for a centered Gaussian vector with i.i.d. entries, both conditioned on (a general Wigner matrix), and unconditioned when is a GOE matrix. Our results validate (in a certain region) and correct (in another region), the prediction obtained by the mathematically non-rigorous replica method in Fyodorov and Doussal.
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