Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
肖惠 博士,Univeristé de Bretagne Sud, France
Inviter:
巩馥洲 研究员
Title:
Precise large deviation asymptotics for products of random matrices
Time & Venue:
2018.7.4 15:00 N613
Abstract:
For a sum S_n of independent random variables, Bahadur and Rao and Petrov have established equivalents for large deviation probabilities P(S_n≥n(q+l)), where q is fixed and l is vanishing as n→∞. These milestone results have numerous applications in a variety of problems in pure and applied probability. The goal of this paper is to obtain analogous statements for the product G_{n}:=g_{n}… g_{1}, where (g_{n})_{n≥1} is a sequence of independent and identically distributed d×d real random matrices. We deal with the norm |G_n x| with x a starting point on the unit sphere in R^d and with the entries G_n^{j,i} for both invertible matrices and positive matrices. As applications we improve previous results on large deviation principles for the norm and the scalar product and obtain precise large deviations in a local limit theorem.