Donald Robertson
Ohio State University
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Publication
Featured researches published by Donald Robertson.
Combinatorics, Probability & Computing | 2017
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, for example the class of finite simple groups. This is deduced from a strong double recurrence theorem for two commuting measure-preserving actions of a minimally almost periodic (not necessarily amenable or locally compact) group on a (not necessarily separable) probability space.
Journal of Functional Analysis | 2016
Vitaly Bergelson; J.C. Christopherson; Donald Robertson; Pavel Zorin-Kranich
Abstract We characterize those locally compact, second countable, amenable groups in which a density version of Hindmans theorem holds and those countable, amenable groups in which a two-sided density version of Hindmans theorem holds. In both cases the possible failure can be attributed to an abundance of finite-dimensional unitary representations, which allows us to construct sets with large density that do not contain any shift of a set of measurable recurrence, let alone a shift of a finite products set. The possible success is connected to the ergodic–theoretic phenomenon of weak mixing via a two-sided version of the Furstenberg correspondence principle. We also construct subsets with large density that are not piecewise syndetic in arbitrary non-compact amenable groups. For countably infinite amenable groups, the symbolic systems associated to such sets admit invariant probability measures that are not concentrated on their minimal subsystems.
Israel Journal of Mathematics | 2016
Vitaly Bergelson; Donald Robertson
Journal D Analyse Mathematique | 2016
Donald Robertson
Ergodic Theory and Dynamical Systems | 2016
Vitaly Bergelson; Donald Robertson
arXiv: Dynamical Systems | 2018
Jon Chaika; Donald Robertson
arXiv: Dynamical Systems | 2018
Leonard Carapezza; Marco López; Donald Robertson
arXiv: Combinatorics | 2018
Joel Moreira; Florian Karl Richter; Donald Robertson
Archive | 2018
Joel Moreira; Florian Karl Richter; Donald Robertson
arXiv: Dynamical Systems | 2017
Joel Moreira; Florian Karl Richter; Donald Robertson