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Seminar
FIELD Mathematics
DATE January 12 (Wed), 2022
TIME 16:00-17:00
PLACE Online
SPEAKER Park, Kiho
HOST Byun, Sungsoo
INSTITUTE  
TITLE [GS_M_APP] Transfer operators and limit laws for typical cocycles
ABSTRACT We consider a dynamical system f \colon X \to X and a matrix cocycle A \colon X \to GL_d(R), and study the product A(f^nx) \ldots A(x) of A along the orbit of x. In particular, we will show that for a class of dynamical systems f and a class of matrix cocycles A the product A(f^nx) \ldots A(x) satisfies various limit laws, such as the central limit theorem and the large deviation principle (with respect to certain invariant measures on X, including the measure of maximal entropy). We also establish the analytic dependence of the top Lyapunov exponent on the invariant measures. The transfer operator and its spectral properties play key roles in establishing these limit laws. This is joint work with Mark Piraino.
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