|Date: Monday, October 21, 2013
Location: 3096 East Hall (4:00 PM to 5:00 PM)
Title: Stochastic properties of holomorphic maps
Abstract: In this talk, I shall discuss some statistical properties of random holomorphic endomorphisms of the complex projective space. For a sequence of i.i.d. holomorphic endomorphisms of fixed algebraic degree d>1, we can construct a measure which describes asymptotic distribution of time-averages and asymptotic distribution of pre-images of a generic point. Moreover, under a natural assumption on the distribution of the sequence, almost surely these measures have Holder continuous quasi-potentials. Furthermore, if the distribution is compactly supported in the set of holomorphic endomorphisms then we obtain exponential decay of correlations and this in turn implies Central Limit Theorem for Holder continuous and d.s.h. observables.
Speaker: Turgay Bayraktar
Institution: Indiana University