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Dive into the research topics where Robin D. Tucker-Drob is active.

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Featured researches published by Robin D. Tucker-Drob.


Ergodic Theory and Dynamical Systems | 2013

Ultraproducts of measure preserving actions and graph combinatorics

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

Borel structurability on the 2-shift of a countable group

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

BROOKS’ THEOREM FOR MEASURABLE COLORINGS

Clinton T. Conley; Andrew S. Marks; Robin D. Tucker-Drob

We generalize Brookss theorem to show that if


Mathematische Annalen | 2018

Følner tilings for actions of amenable groups

Clinton T. Conley; Steve Jackson; David Kerr; Andrew S. Marks; Brandon Seward; Robin D. Tucker-Drob

G


arXiv: Group Theory | 2012

Shift-minimal groups, fixed price 1, and the unique trace property

Robin D. Tucker-Drob

is a Borel graph on a standard Borel space


Ergodic Theory and Dynamical Systems | 2015

Weak equivalence and non-classifiability of measure preserving actions

Robin D. Tucker-Drob

X


Bulletin of The London Mathematical Society | 2014

Invariant random subgroups of strictly diagonal limits of finite symmetric groups

Simon Thomas; Robin D. Tucker-Drob

of degree bounded by


arXiv: Group Theory | 2014

Invariant means and the structure of inner amenable groups

Robin D. Tucker-Drob

d \geq 3


Israel Journal of Mathematics | 2013

On a co-induction question of Kechris

Lewis Bowen; Robin D. Tucker-Drob

which contains no


Advances in Mathematics | 2016

Weak containment rigidity for distal actions

Adrian Ioana; Robin D. Tucker-Drob

(d+1)

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Clinton T. Conley

Carnegie Mellon University

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Lewis Bowen

University of Texas at Austin

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Adrian Ioana

University of California

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Alexander S. Kechris

California Institute of Technology

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Steve Jackson

University of North Texas

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