Nikita Moriakov

collaborators

3 papers

math.DS2017

On effective Birkhoff's ergodic theorem for computable actions of amenable groups

Nikita Moriakov

We introduce computable actions of computable groups and prove the following versions of effective Birkhoff's ergodic theorem. Let $Γ$ be a computable amenable group, then there al…

math.DS2016

Hochman's upcrossing theorem for groups of polynomial growth

Nikita Moriakov

Consider a stochastic process $(S_{[a_{i}, b_{i}]})_{[a_{i}, b_{i}] \subset N}$ , which is indexed by the collection of all nonempty intervals $[a_{i}, b_{i}] \subset N$ and whic…

math.DS2016

Fluctuations of Ergodic Averages for Actions of Groups of Polynomial Growth

Nikita Moriakov

It was shown by S. Kalikow and B. Weiss that, given a measure-preserving action of $Z^{d}$ on a probability space $X$ and a nonnegative measurable function $f$ on $X$ , the p…