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Tuesday, March 24, 2015

12:00 PM - 1:00 PM (ET)

ESC 638

Event Type

Academic Calendar

Contact

David Constantine, x2170

Department

Math CS DnA Seminar

Link

https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=63376

Abstract: We will consider two problems involving ergodic sums of bounded-variation functions on the unit circle, where the underlying transformation is irrational rotation. First, while the ergodic sums must return to a small range of values at prescribed times (the Denjoy-Koksma inequality), we may investigate the nondecreasing function which tracks the largest sum (in absolute value) achieved through a given time. We will provide a generic asymptotic upper bound on this function. If we restrict our attention to a specific bounded-variation function (a system known as the infinite staircase), we may also place an almost-sure lower bound on the growth of this function. Second, F. Huveneers established for every rotation the existence of a sequence of times for which the ergodic sums in the infinite staircase obey a central limit theorem, although his technique was only somewhat explicit in determining exactly which times could create a central limit theorem. We will discuss how to make his results more specific and stronger, while also extending them to other piecewise-constant functions (albeit restricted to almost-every instead of every rotation).