Wednesday, October 9, 2013

A final play of the quantitative Birkhoff ergodic theorem leitmotif

Silvius Klein

Abstract: After introducing the main players - the BMO space, the Hilbert transform, uniformly distributed sequences with their discrepancy estimates, after having them warm up and rehearse - by establishing such a quantitative result for our baby subharmonic function u (z) = log | z - 1 |, it is now high time to put the whole ensemble to work on general subharmonic functions, like the ones associated to an analytic, quasi-periodic, linear co-cycle. The output will be a quantitative estimate on the set of phases for which the Birkhoff averages of a subharmonic function deviate from its mean, which in turn can be used to establish large deviations estimates for iterates of the co-cycle, which when combined with ... but I am beginning to repeat myself ...

Wednesday, October 9, 2013
Time: 10h30
Room: B3-01, Complexo Interdisciplinar, UL