Anush Tserunyan

Անուշ Ծերունյան

Rooted in logic and descriptive set theory, my research lies in the nexus of countable Borel equivalence relations, ergodic theory, measured group theory, measurable graph combinatorics, percolation theory, and geometric group theory.

Preprints

Heavy repulsion of clusters in Bernoulli percolation [arXiv] (2025+)
▻with Alexandra (Sasha) Bell, Tasmin Chu, Owen Rodgers, and Grigory Terlov

Nonamenable subforests of multi-ended quasi-pmp graphs [arXiv] (2022+)
▻with Ruiyuan (Ronnie) Chen and Grigory Terlov

Edge sliding and ergodic hyperfinite decomposition [arXiv] (2017+)
▻with Benjamin Miller

Publications

Tree-like graphings, wallings, and median graphings of equivalence relations [arXiv, doi]
▻with Ruiyuan (Ronnie) Chen, Antoine Poulin, and Ran Tao

Forum of Mathematics, Sigma, 2025;13:e64
A backward ergodic theorem along trees and its consequences for free group actions [arXiv, doi]
▻with Jenna Zomback

Journal of European Math. Soc. (JEMS), 2025, published online first
A ratio ergodic theorem via tiling and uniformly syndetic markers [arXiv, doi]
▻with Benjamin Miller

Ergodic Theory and Dynamical Systems: Proceedings of the Workshops University of North Carolina at Chapel Hill 2021, edited by Idris Assani, Berlin, Boston: De Gruyter (2024), pp. 99–116.
Pairs of disjoint matchings and related classes of graphs [arXiv, doi]
▻with H. Guo, K. Kaempen, Z. Mo, S. Qunell, J. Rogge, C. Song, J. Zomback

Involve, a Journal of Mathematics 16-2 (2023), 249–264

Mixing and double recurrence in probability groups [arXiv, doi]
Fundamenta Mathematicae 260 (2023), 77–98
Pointwise ergodic theorem for locally countable quasi-pmp graphs [arXiv, doi]
Journal of Modern Dynamics, 18 (2022), 609–655
Characterization of saturated graphs related to pairs of disjoint matchings [arXiv, doi]
▻with Zhengda Mo, Samuel Qunell, and Jenna Zomback

Illinois J. Math. 66(1): 59–77 (2022)
Independent sets in algebraic hypergraphs [arXiv, doi]
▻with Anton Bernshteyn and Michelle Delcourt

Journal of European Math. Soc. (JEMS), 24(1):1–35, 2022, published online in 2021.
A descriptive construction of trees and Stallings' theorem [arXiv, doi]
Trends in set theory, Contemporary Mathematics, vol. 752 (2020), Amer. Math. Soc., Providence, RI, pp. 191–207
A short nonalgorithmic proof of the containers theorem for hypergraphs [arXiv, doi]
▻with Anton Bernshteyn, Michelle Delcourt, and Henry Towsner

Proceedings of the American Math. Soc., vol. 147 (2019), pp. 1739–1749

A Ramsey theorem on semigroups and a general van der Corput lemma [arXiv, doi]
Journal of Symbolic Logic, vol. 81 (2016), no. 2, pp. 718–741
Finite generators for countable group actions in the Borel and Baire category settings [arXiv, doi]
Advances in Mathematics, vol. 269 (2015), pp. 585–646
Characterization of a class of graphs related to pairs of disjoint matchings [arXiv, doi]
Discrete Mathematics, vol. 309 (2009), no. 4, pp. 693–713
On edge-disjoint pairs of matchings [arXiv, doi]
▻with Vahan Mkrtchyan and Vahé Musoyan

Discrete Mathematics, vol. 308 (2008), no. 23, pp. 5823–5828

Ph.D. Thesis

Finite generators for countable group actions; Finite index pairs of equivalence relations; Complexity measures for recursive programs [pdf, ProQuest]: UCLA (May, 2013)

Other writing

The following are some things I've written that are either partially published or not (currently) intended for publication.

A descriptive set theorist's proof of the pointwise ergodic theorem [arXiv]
Oberwolfach, Germany (2017)
Realizations of graphs in a Hilbert space [pdf]
(with Terence Tao) Banff International Research Station, Canada (July, 2015)
The Effros space of a σ-Polish space is standard Borel [pdf]
UIUC (January, 2014)
Countable compact Hausdorff spaces are Polish [pdf]
UCLA (March, 2013)
Segal's effective witness to measure-hyperfiniteness [pdf]
Caltech (Fall, 2012)
Hjorth's proof of the embeddability of hyperfinite equivalence relations into E₀ [pdf]
UCLA (Fall, 2010)

Contributions in others' works

Y. Moschovakis, Abstract Recursion and Intrinsic Complexity, to appear in the ASL Lecture Notes in Logic (2018) [pdf]
Section 3B consists of the results of Part 3 of my Ph.D. thesis on complexity measures for recursive programs.

UCLA (Fall, 2009)
A. Kechris, The spaces of measure preserving equivalence relations and graphs, preprint (2017) [pdf]
Sections 3, 6, 19 contain some of my results regarding the weak and strong topologies, the discontinuity of the map from actions to equivalence relations, and subtreeings of treeings of an equivalence relation.

Caltech (Spring, 2013)
M. Lupini, Polish groupoids and functorial complexity, Trans. of the Amer. Math. Soc., 369 (2017), no. 9, 6683–6723 [arXiv]
Appendix consists of my proof of the Effros space of a σ-Polish space being standard Borel. [pdf]

UIUC (January, 2014)