Research Papers

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62.	Locally compact sofic groups	with Peter Burton	To appear in Israel J. of Math.	arXiv
61.	A multiplicative ergodic theorem for von Neumann algebra valued cocycles	with Ben Hayes, Yuqing (Frank) Lin	Comm. Math. Phys. 384 (2021), no. 2, 1291–1350.	arXiv
60.	A topological dynamical system with two different positive sofic entropies	with Dylan Airey and Yuqing (Frank) Lin	to appear in Trans. Amer. Math. Soc.	arXiv	video	talk slides
59.	Flexible stability and nonsoficity	with Peter Burton	Trans. Amer. Math. Soc. 373 (2020), no. 6, 4469–4481.	arXiv
58.	Failure of the L^1 pointwise ergodic theorem for PSL(2,R).	with Peter Burton	Geom. Dedicata 207 (2020), 61–80.	arXiv
57.	Sofic homological invariants and the Weak Pinsker Property		to appear in Amer. J. Math.	arXiv
56.	Superrigidity, measure equivalence, and weak Pinsker entropy	with Robin Tucker-Drob	to appear in Groups, Geometry and Dynamics.	arXiv
55.	A brief introduction to sofic entropy theory		Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. III. Invited lectures, 1847–1866, World Sci. Publ., Hackensack, NJ, 2018	arXiv	video	talk slides
54.	Finitary random interlacements and the Gaboriau-Lyons problem		Geom. Funct. Anal. 29 (2019), no. 3, 659–689.	arXiv
53.	All properly ergodic Markov chains over a free group are orbit equivalent		Unimodularity in randomly generated graphs, 155–174, Contemp. Math., 719, Amer. Math. Soc., Providence, RI, 2018.	arXiv
52.	The space of stable weak equivalence classes of measure-preserving actions	with Robin Tucker-Drob	J. Funct. Anal. 274 (2018), no. 11, 3170–3196.	arXiv
51.	Examples in the entropy theory of countable group actions		Ergodic Theory Dynam. Systems 40 (2020), no. 10, 2593–2680.	arXiv
50.	Invariant random subgroups of semidirect products	with Ian Biringer and Omer Tamuz	Ergodic Theory Dynam. Systems 40 (2020), no. 2, 353–366.To appear in Ergodic Theory and Dynamical Systems.	arXix
49.	Zero entropy is generic		Entropy 18 (2016), no. 6, Paper No. 220, 20 pp.	arXiv
48.	Integrable orbit equivalence rigidity for free groups		Israel J. Math. 221 (2017), no. 1, 471–480.	arXiv
47.	Hyperbolic geometry and pointwise ergodic theorems	with Amos Nevo	Ergodic Theory Dynam. Systems 39 (2019), no. 10, 2689–2716.	arXiv
46.	von Neumann's problem and extensions of non-amenable equivalence relations	with Daniel Hoff and Adrian Ioana	Groups Geom. Dyn. 12 (2018), no. 2, 399–448.	arXiv
45.	Simple and large equivalence relations		Proc. Amer. Math. Soc. 145 (2017), no. 1, 215–224.	arXiv
44.	Equivalence relations that act on bundles of hyperbolic spaces		Ergodic Theory Dynam. Systems 38 (2018), no. 7, 2447–2492.	arXiv
43.	Mean convergence of Markovian spherical averages for measure-preserving actions of the free group	with Alexander Bufetov and Olga Romaskevich	Geom. Dedicata 181 (2016), 293–306.	arXiv
42.	Property (T) and the Furstenberg entropy of nonsingular actions	with Yair Hartman and Omer Tamuz	Proc. Amer. Math. Soc. 144 (2016), no. 1, 31–39.	arXiv
41.	Generic stationary measures and actions	with Yair Hartman and Omer Tamuz	Trans. Amer. Math. Soc. 369 (2017), no. 7, 4889--4929.	arXiv
40.	Characteristic random subgroups of geometric groups and free abelian groups of infinite rank	with Rostislav Grigorchuk and Rostyslav Kravchenko	Trans. Amer. Math. Soc. 369 (2017), no. 2, 755–781.	arXiv
39.	L1-measure equivalence and group growth (Appendix to: Integrable measure equivalence for groups of polynomial growth by Tim Austin)		Groups Geom. Dyn. 10 (2016), no. 1, 117–154.	arXiv
38.	Weak density of orbit equivalence classes of free group actions		Groups Geom. Dyn. 9 (2015), no. 3, 811–830.	arXiv
37.	Cheeger constants and L2-Betti numbers		Duke Math. J. 164 (2015), no. 3, 569–615.	arXiv
36.	von-Neumann and Birkhoff ergodic theorems for negatively curved groups	with Amos Nevo	Ann. Sci. Éc. Norm. Supér. (4) 48 (2015), no. 5, 1113–1147.	arXiv
35.	Amenable equivalence relations and the construction of ergodic averages for group actions	with Amos Nevo	J. Anal. Math. 126 (2015), 359–388.	arXiv
34.	Entropy theory for sofic groupoids I: the foundations		Journal d'Analyse Mathématique October 2014, Volume 124, Issue 1, pp 149--233.	arXiv
33.	The type and stable type of the boundary of a Gromov hyperbolic group		Geometriae Dedicata, October 2014, Volume 172, Issue 1, pp 363--386.	arXiv
32.	A horospherical ratio ergodic theorem for actions of free groups	with Amos Nevo	Groups Geom. Dyn. 8(2):331--353, 2014.	arXiv
31.	Invariant random subgroups of lamplighter groups (new version as of Sept 2, 2013)	with Rostislav Grigorchuk and Rostyslav Kravchenko	Israel J. Math. 207 (2015), no. 2, 763–782.	arXiv
30.	Invariant random subgroups of the free group		Groups Geom. Dyn. 9 (2015), no. 3, 891–916.	arXiv
29.	A Juzvinskiĭ Addition Theorem for Finitely Generated Free Group Actions	with Yonatan Gutman	Ergodic Theory Dynam. Systems 34 (2014), no. 1, 95–109.	arXiv
28.	Harmonic models and spanning forests of residually finite groups	with Hanfeng Li	J. Funct. Anal. 263, no. 7, (2012), 1769--1808	arXiv
27.	On a co-induction question of Kechris	with Robin Tucker-Drob	Israel J. of Math. March 2013, Volume 194, Issue 1, pp 209--224	arXiv
26.	Random walks on coset spaces with applications to Furstenberg entropy		Invent. Math. Volume 196, Issue 2 (2014), Page 485-510	arXiv
25.	Pointwise ergodic theorems beyond amenable groups	with Amos Nevo	Ergod. Th. and Dynam. Sys. (2013), 33, 777--820	arXiv
24.	Geometric covering arguments and ergodic theorems for free groups	with Amos Nevo	L’Enseignement Mathématique, Volume 59, Issue 1/2, 2013, pp. 133--164	arXiv
23.	Every countably infinite group is almost Ornstein		Dynamical systems and group actions, 67–78, Contemp. Math., 567, Amer. Math. Soc., Providence, RI, 2012.	arXiv
22.	Sofic entropy and amenable groups		Ergodic Theory Dynam. Systems 32 (2012), no. 2, 427–466	arXiv
21.	Stable orbit equivalence of Bernoulli shifts over free groups		Groups Geom. Dyn. 5 (2011), no. 1, 17–38.	arXiv
20.	Orbit equivalence, coinduced actions and free products		Groups Geom. Dyn. 5 (2011), no. 1, 1–15.	arXiv
19.	Entropy for expansive algebraic actions of residually finite groups		Ergodic Theory Dynam. Systems. 31 (2011), no. 3, 703--718.	arXiv
18.	Weak isomorphisms between Bernoulli shifts		Israel J. of Math, (2011) Volume 183, Number 1, 93-102	arXiv
17.	Nonabelian free group actions: Markov processes, the Abramov-Rohlin formula and Yuzvinskii's formula		Ergodic Theory Dynam. Systems 30 (2010), no. 6, 1629--1663.	arXiv
17.	Corrigendum	with Yonatan Gutman	Ergodic Theory and Dynam. Systems 33 Issue 02 / April 2013, pp 643 - 645.	arXiv
16.	The ergodic theory of free group actions: entropy and the f-invariant.		Groups Geom. Dyn. 4 (2010), no. 3, 419--432	arXiv
15.	A new measure conjugacy invariant for actions of free groups		Ann. of Math., vol. 171 (2010), No. 2, 1387--1400.	arXiv
14.	Measure conjugacy invariants for actions of countable sofic groups		J. Amer. Math. Soc., 23 (2010), 217-245.	arXiv
13.	Invariant measures on the space of horofunctions of a word hyperbolic group		Ergodic Theory Dynam. Systems. 30 (2010), no. 1, 97--129.	arXiv
12.	Free groups in lattices		Geometry & Topology, 13, (2009), 3021--3054.	arXiv
11.	A generalization of the prime geodesic theorem to counting conjugacy classes of free subgroups		Geom. Dedicata, 124, (2007), 37--67.	arXiv
10.	A Solidification Phenomenon in Random Packings	with Russell Lyons, Charles Radin and Peter Winkler	SIAM J. Math. Anal. 38 (2006), no. 4, 1075--1089.
9.	Fluid/Solid Transition in a Hard-Core System	with Russell Lyons, Charles Radin and Peter Winkler	Phys. Rev. Lett. 96, 025701 (2006)
8.	Uniqueness and symmetry in problems of optimally dense packings	with Charles Holton, Charles Radin and Lorenzo Sadun	Math. Phys. Electron. J. 11 (2005), Paper 1, 34 pp.	arXiv
7.	On the Gromov Norm of the Product of Two Surfaces	with Mike Develin, Jesus De Loera and Francisco Santos	Topology 44 (2005), no. 2, 321--339. erratum: Topology 47 (2008), no. 6, 471--472.	arXiv
6.	Couplings of Uniform Spanning Forests		Proc. Amer. Math. Soc. 132 (2004), no. 7, 2151--2158.	arXiv
5.	Optimally Dense Packings of Hyperbolic Space	with Charles Radin	Geom. Dedicata 104 (2004), 37--59.	arXiv
4.	On the existence of completely saturated packings and completely reduced coverings		Geom. Dedicata 98 (2003), 211--226.	arXiv
3.	Densest Packing of Equal Spheres in Hyperbolic Space	with Charles Radin	Discrete Comput. Geom. 29 (2003), no. 1, 23--39.
2.	Periodicity and Circle Packing in the Hyperbolic Plane		Geom. Dedicata 102 (2003), 213--236.	arXiv
1.	Circle Packing in Hyperbolic Space		Math. Phys. Electron. J. 6 (2000), Paper 6, 10 pp. (electronic).

This material is based upon work supported by the National Science Foundation under Grants No. 0901835 (9/1/09-2/28/10), 0968762 (9/1/09-8/31/12), 0954606 (5/15/10-4/30/15) and 1500389 (May 2015-April 2018). The collaborative work with Amos Nevo was supported by the Binational Science Foundation under Grant No. 2008274 (9/1/09-8/31/13).

Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF) or the Binational Science Foundation.