Robin D. Tucker-Drob
Texas A&M University
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Publication
Featured researches published by Robin D. Tucker-Drob.
Ergodic Theory and Dynamical Systems | 2013
Clinton T. Conley; Alexander S. Kechris; Robin D. Tucker-Drob
Ultraproducts of measure preserving actions of countable groups are used to study the graph combinatorics associated with such actions, including chromatic, independence and matching numbers. Applications are also given to the theory of random colorings of Cayley graphs and sofic actions and equivalence relations.
Annals of Pure and Applied Logic | 2016
Brandon Seward; Robin D. Tucker-Drob
Abstract We show that for any infinite countable group G and for any free Borel action G ↷ X there exists an equivariant class-bijective Borel map from X to the free part Free ( 2 G ) of the 2-shift G ↷ 2 G . This implies that any Borel structurability which holds for the equivalence relation generated by G ↷ Free ( 2 G ) must hold a fortiori for all equivalence relations coming from free Borel actions of G. A related consequence is that the Borel chromatic number of Free ( 2 G ) is the maximum among Borel chromatic numbers of free actions of G. This answers a question of Marks. Our construction is flexible and, using an appropriate notion of genericity, we are able to show that in fact the generic G-equivariant map to 2 G lands in the free part. As a corollary we obtain that for every ϵ > 0 , every free p.m.p. action of G has a free factor which admits a 2-piece generating partition with Shannon entropy less than ϵ. This generalizes a result of Danilenko and Park.
arXiv: Logic | 2016
Clinton T. Conley; Andrew S. Marks; Robin D. Tucker-Drob
We generalize Brookss theorem to show that if
Mathematische Annalen | 2018
Clinton T. Conley; Steve Jackson; David Kerr; Andrew S. Marks; Brandon Seward; Robin D. Tucker-Drob
G
arXiv: Group Theory | 2012
Robin D. Tucker-Drob
is a Borel graph on a standard Borel space
Ergodic Theory and Dynamical Systems | 2015
Robin D. Tucker-Drob
X
Bulletin of The London Mathematical Society | 2014
Simon Thomas; Robin D. Tucker-Drob
of degree bounded by
arXiv: Group Theory | 2014
Robin D. Tucker-Drob
d \geq 3
Israel Journal of Mathematics | 2013
Lewis Bowen; Robin D. Tucker-Drob
which contains no
Advances in Mathematics | 2016
Adrian Ioana; Robin D. Tucker-Drob
(d+1)