1.8k citations · 1.8k across the 13 of their papers we have counts for
17 papers
Ramsey, expanders, and Borel chromatic numbers
Jan Grebík, Zoltán Vidnyánszky
We construct bounded degree acyclic Borel graphs with large Borel chromatic number using a graph arising from Ramsey theory and limits of expander sequences.
Measurable tilings by abelian group actions
Jan Grebík, Rachel Greenfeld, Václav Rozhoň +1
Let be a measure space with a measure-preserving action of an abelian group . We consider the problem of understanding the structure of measurable…
Borel equivalence relations induced by actions of tsi Polish groups
Jan Grebík
We study Borel equivalence relations induced by Borel actions of tsi Polish groups on standard Borel spaces. We characterize when such an equivalence relation admits classification…
Classification of Local Problems on Paths from the Perspective of Descriptive Combinatorics
Jan Grebík, Václav Rozhoň
We classify which local problems with inputs on oriented paths have so-called Borel solution and show that this class of problems remains the same if we instead require a measurabl…
Local Problems on Grids from the Perspective of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics
Jan Grebík, Václav Rozhoň
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: com…
Large Deviation Principles for Block and Step Graphon Random Graph Models
Jan Grebík, Oleg Pikhurko
Borgs, Chayes, Gaudio, Petti and Sen [arXiv:2007.14508] proved a large deviation principle for block model random graphs with rational block ratios. We strengthen their result by a…