40 citations · 489 across the 52 of their papers we have counts for
13 papers · 1 filter
A double return times theorem
Pavel Zorin-Kranich
We prove that for any bounded functions on a measure-preserving dynamical system and any distinct integers , for almost every the sequence $$ f_1(T…
A uniform nilsequence Wiener-Wintner theorem for bilinear ergodic averages
Pavel Zorin-Kranich
We show that a -linear pointwise ergodic theorem on an ergodic measure-preserving system implies a uniform -linear nilsequence Wiener-Wintner theorem on that system. The assu…
Triangles in cartesian squares of quasirandom groups
Vitaly Bergelson, Donald Robertson, Pavel Zorin-Kranich
We prove that triangular configurations are plentiful in large subsets of cartesian squares of finite quasirandom groups from classes having the quasirandom ultraproduct property,…
A random pointwise ergodic theorem with Hardy field weights
Ben Krause, Pavel Zorin-Kranich
Let be the random increasing sequence of natural numbers which takes each value independently with probability , , and let , .…
Finite Products Sets and Minimally Almost Periodic Groups
Vitaly Bergelson, Cory Christopherson, Donald Robertson +1
We construct, in locally compact, second countable, amenable groups, sets with large density that fail to have certain combinatorial properties. For the property of being a shift o…
Ergodic theorems for polynomials in nilpotent groups
Pavel Zorin-Kranich
The principal results proved in this expository thesis are the IP polynomial Szemerédi theorem for nilpotent groups and the multiple term return times theorem with nilsequence weig…
Lower bound in the Roth theorem for amenable groups
Qing Chu, Pavel Zorin-Kranich
Let , be two commuting probability measure-preserving actions of a countable amenable group such that the group spanned by these actions acts ergodically. We show that $…
Multiple recurrence for non-commuting transformations along rationally independent polynomials
Nikos Frantzikinakis, Pavel Zorin-Kranich
We prove a multiple recurrence result for arbitrary measure-preserving transformations along polynomials in two variables of the form , with rationally independent '…
Return times theorem for amenable groups
Pavel Zorin-Kranich
We extend Bourgain's return times theorem to arbitrary locally compact second countable amenable groups. The proof is based on a version of the Bourgain--Furstenberg--Katznelson--O…
Cube spaces and the multiple term return times theorem
Pavel Zorin-Kranich
We give a new proof of Rudolph's multiple term return times theorem based on Host-Kra structure theory. Our approach provides characteristic factors for all terms, works for arbitr…
Uniformity in the Wiener-Wintner theorem for nilsequences
Tanja Eisner, Pavel Zorin-Kranich
We prove a uniform extension of the Wiener-Wintner theorem for nilsequences due to Host and Kra and a nilsequence extension of the topological Wiener-Wintner theorem due to Assani.…
A nilpotent IP polynomial multiple recurrence theorem
Pavel Zorin-Kranich
We generalize the IP-polynomial Szemerédi theorem due to Bergelson and McCutcheon and the nilpotent Szemerédi theorem due to Leibman. Important tools in our proof include a general…
Norm convergence of multiple ergodic averages on amenable groups
Pavel Zorin-Kranich
We apply Walsh's method for proving norm convergence of multiple ergodic averages to arbitrary amenable groups. We obtain convergence in the uniform Cesàro sense for their polynomi…