Borel asymptotic dimension and hyperfinite equivalence relations
CT Conley, SC Jackson, AS Marks… - Duke Mathematical …, 2023 - projecteuclid.org
A long-standing open problem in the theory of hyperfinite equivalence relations asks
whether the orbit equivalence relation generated by a Borel action of a countable amenable …
whether the orbit equivalence relation generated by a Borel action of a countable amenable …
Local problems on grids from the perspective of distributed algorithms, finitary factors, and descriptive combinatorics
J Grebík, V Rozhoň - Advances in Mathematics, 2023 - Elsevier
We present an intimate connection among the following fields:(a) distributed local
algorithms: coming from the area of computer science,(b) finitary factors of iid processes …
algorithms: coming from the area of computer science,(b) finitary factors of iid processes …
[图书][B] The theory of countable Borel equivalence relations
AS Kechris - 2024 - pma.caltech.edu
The theory of definable equivalence relations has been a very active area of research in
descriptive set theory during the last three decades. It serves as a foundation of a theory of …
descriptive set theory during the last three decades. It serves as a foundation of a theory of …
Distributed algorithms, the Lovász Local Lemma, and descriptive combinatorics
A Bernshteyn - Inventiones mathematicae, 2023 - Springer
In this paper we consider coloring problems on graphs and other combinatorial structures on
standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings …
standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings …
Borel combinatorics of locally finite graphs
O Pikhurko - arXiv preprint arXiv:2009.09113, 2020 - arxiv.org
We provide a gentle introduction, aimed at non-experts, to Borel combinatorics that studies
definable graphs on topological spaces. This is an emerging field on the borderline between …
definable graphs on topological spaces. This is an emerging field on the borderline between …
Extremal aspects of graph and hypergraph decomposition problems.
Extremal aspects of graph and hypergraph decomposition problems. Page 245 Extremal aspects
of graph and hypergraph decomposition problems Stefan Glock Daniela Kühn Deryk Osthus …
of graph and hypergraph decomposition problems Stefan Glock Daniela Kühn Deryk Osthus …
Probabilistic constructions in continuous combinatorics and a bridge to distributed algorithms
A Bernshteyn - Advances in Mathematics, 2023 - Elsevier
The probabilistic method is a technique for proving combinatorial existence results by
means of showing that a randomly chosen object has the desired properties with positive …
means of showing that a randomly chosen object has the desired properties with positive …
Borel versions of the Local Lemma and LOCAL algorithms for graphs of finite asymptotic separation index
A Bernshteyn, F Weilacher - arXiv preprint arXiv:2308.14941, 2023 - arxiv.org
Asymptotic separation index is a parameter that measures how easily a Borel graph can be
approximated by its subgraphs with finite components. In contrast to the more classical …
approximated by its subgraphs with finite components. In contrast to the more classical …
Descriptive combinatorics, computable combinatorics, and ASI algorithms
L Qian, F Weilacher - arXiv preprint arXiv:2206.08426, 2022 - arxiv.org
We introduce new types of local algorithms, which we call" ASI Algorithms", and use them to
demonstrate a link between descriptive and computable combinatorics. This allows us to …
demonstrate a link between descriptive and computable combinatorics. This allows us to …