Research Papers

Back to Home Page

54.
Finitary random interlacements and the Gaboriau-Lyons problem


arXiv
53.
All properly ergodic Markov chains over a free group are orbit equivalent

submitted
arXiv
52.
The space of stable weak equivalence classes of measure-preserving actions
with Robin Tucker-Drob submitted
arXiv
51.
Examples in the entropy theory of countable group actions

submitted
arXiv
50.
Invariant random subgroups of semidirect products
with Ian Biringer and Omer Tamuz
submitted 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
to appear in Israel J. of Math. arXiv
47.
Hyperbolic geometry and pointwise ergodic theorems
with Amos Nevo submitted
arXiv
46.
von Neumann's problem and extensions of non-amenable equivalence relations
with Daniel Hoff and Adrian Ioana
submitted
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

to appear in Ergodic Theory and Dynamical Systems
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 to appear in Transactions of the AMS 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 , 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


title
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

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) and 0954606 (5/15/10-4/30/15). 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.