Lower bounds for generalized upcrossings of ergodic averages

Convergence of Diagonal Ergodic Averages

The case l = 1 is the mean ergodic theorem, and the result can be viewed as a generalization of that theorem. The l = 2 case was proven by Conze and Lesigne [Conze and Lesigne, 1984], and various special cases for higher l have been shown by Zhang [Zhang, 1996], Frantzikinakis and Kra [Frantzikinakis and Kra, 2005], Lesigne [Lesigne, 1993], and Host and Kra [Host and Kra, 2005]. Tao’s argument ...

Local Stability of Ergodic Averages

We consider the extent to which one can compute bounds on the rate of convergence of a sequence of ergodic averages. It is not difficult to construct an example of a computable Lebesgue-measure preserving transformation of [0, 1] and a characteristic function f = χA such that the ergodic averages Anf do not converge to a computable element of L ([0, 1]). In particular, there is no computable bo...

Some Lower Bounds for Estrada Index

Lower bounds for generalized Ginzburg-Landau functionals

Ergodic Theorems for Random Group Averages

This is an earlier, but more general, version of ”An L Ergodic Theorem for Sparse Random Subsequences”. We prove an L ergodic theorem for averages defined by independent random selector variables, in a setting of general measure-preserving group actions. A far more readable version of this paper is in the works.