publications
49. (with Josh Frisch and Mark Rychnovsky) Poisson boundary for upper-triangular matrices
https://arxiv.org/abs/2305.13231
48. (with Josh Frisch),
Poisson boundary of group extensions,
47. (with Tianyi Zheng), Law of large numbers for the drift of two-dimensional wreath product, Probability Theory and Related Fields 182(2)
https://arxiv.org/abs/2011.07628
46 (with Ivan Mitrofanov), Assouad-Nagata dimension and gap for ordered metric spaces, tCommentarii Mathematici Helvetici, Comment. Math. Helv. 98 (2023), no. 2, 217–260.
https://arxiv.org/abs/2109.12181
45. (with Ivan Mitrofanov), Spaces that can be ordered effectively: virtually free groups and hyperbolicity, Geom. Dedicata 217, 68,(2023),
https://arxiv.org/abs/2011.01732
44. Erschler, A., Kaimanovich, V.A. Arboreal structures on groups and the associated boundaries. Geom. Funct. Anal. 33, 694–748 (2023).
https://arxiv.org/abs/1903.02095
43. (with Tianyi Zheng), Growth of periodic Grigorchuk groups, Inventiones Mathematicae 219 (2020), no. 3, 1069–1155.
https://arxiv.org/abs/1802.09077
42. (with Alexei Kanel'-Belov) No iterated identities satisfied by all finite groups, Israel J. Math. 233 (2019), no. 1, 167–197.
https://arxiv.org/abs/1710.04084
41. (with Tianyi Zheng) Isoperimetric inequalities, shapes of Foelner sets and groups with Shalom's property H_FD, Ann. Inst. Fourier, vol. 70, no 4, 1363--1402, 2020.
https://arxiv.org/abs/1708.04730
40. (with Narutaka Ozawa) Finite dimensional representations constructed from random walks,
Comment. Math. Helv. 93 (2018), no. 3, 555–586.
https://arxiv.org/abs/1609.08585
39. Almost invariance of distributions for random walks on groups, Probab. Theory Related Fields 174 (2019), no. 1-2, 445–476.
http://arxiv.org/abs/1603.01458
38. Iterated identities and iterational depth of groups, Journal of Modern Dynamics, 2015 (9), pp. 257 - 284
http://xxx.lanl.gov/abs/1409.5953
37. (with Laurent Bartholdi) Distortion of imbeddings of groups of intermediate growth into metric spaces,
Proceedings of the American Mathematical Society, 145 (2017), no. 5, 1943–1952.
http://xxx.lanl.gov/abs/1406.5908
36. (with Laurent Bartholdi) Imbeddings into groups of intermediate growth,
GGD, Special issue on the occasion of Pierre de la Harpe's 70-th birthday, Vol. 8, Issue 3, 2014, pp. 605–620 DOI: 10.4171/GGD/241
http://xxx.lanl.gov/pdf/1403.5584.pdf
35. (with Vadim Kaimanovich) Continuity of asymptotic characteristics for random walks on hyperbolic groups, Functional Analysis and
its Applications, Vol.47, issue 2, 2013, pp 152-156
34. (with Laurent Bartholdi), Limit order for finitely generated groups, Ann. Inst. Fourier (Grenoble) 65 (2015), no. 5, 2091–2144.
http://xxx.lanl.gov/abs/1301.4669
33. (with Laurent Bartholdi), Groups of given intermediate growth, Annales de l'institut Fourier 64 (2014), 2003--2036
http://xxx.lanl.gov/abs/1110.3650
32. (with Laurent Bartholdi), Poisson Furstenberg boundary and growth of groups, Probability Theory and Related Fields, 168 (2017), no. 1-2, 347–372.
http://xxx.lanl.gov/abs/1107.5499
31. (with Laurent Bartholdi) Growth of permutational extensions,
Inventiones Mathematicae, Vol. 189, Issue 2 (2012), pp 431-455
http://xxx.lanl.gov/abs/1011.5266
30. (with Balint Toth and Wendelin Werner) Some locally self-interacting walks on the integers,
Probability in Complex Physical Systems (Festschrift for Erwin Bolthausen and Jürgen Gärtner), pp. 313-338, Springer, 2012.
http://xxx.lanl.gov/abs/1011.1102
29. (with Balint Toth and Wendelin Werner) Stuck Walks, Probability Theory and Related Fields 154 (2012), no. 1-2, 149–163.
http://xxx.lanl.gov/abs/1011.1103
28. Poisson-Furstenberg boundaries, large-scale geometry and growth of groups, Proc. of the ICM, Hyderabad, 2010,
27. On contituity of range, drift and entropy for random walks on groups, Proceeding of the conference
Boundary", Graz, Progress in Probability, Vol. 64, 57–66,
2011 Springer Basel AG.
26. (with Anders Karlsson) Homomorphisms constructed from random walks, Ann. Inst. Fourier (Grenoble) 60 (2010), no. 6, 2095–2113
25. Poisson-Furstenberg boundary of random walks
on wreath products and free metabelian groups, Comment. Math. Helv. 86 (2011), no. 1, 113–143.
24. Random mappings of scaled graphs, Probability
Theory and Related Field, vol. 144, no. 3-4, (2009) , pp. 543-579
23. Generalized Brownian bridges, Russian Mathematical Surveys,
2007, v.62, n.3.
22. Generalized wreath products, IMRN, 2006, v. 2006,
n.26, Article ID 57835.
21. Automatically presented groups, Groups, Geometry
and Dynamics, 2007, v.1, n.1, 47-59.
20. Piecewise automatic groups, Duke Math. Journal, 2006, n.134,
v.3, 591-613.
19. Isoperimetry for wreath products of Markov chains and
multiplicity of selfintersections of random walks,
Prob. Theory and Related Fields, vol.136, no.4, 2006,
560-586.
18. On degrees of growth function for groups, Functional Analysis and
its Applications, vol. 39, n. 4, (2005).
17. (with Denis Osin), On fundamental groups of asymptotic
cones, Topology 44, No.4, 827-843 (2005).
16. Critical constants for recurrence of random walks on homogeneous
G-spaces, Ann. Inst. Fourier, 2005, 55, fas.2, 493-509
15. Boundary behavior for groups of subexponential growth, Annals of
Mathematics, 160, no 3, 2004, 1183-1210
14. Liouville property for groups and manifolds, Inventiones Mathematicae,
155, 2004, 55-80.
13. Not residually finite groups of intermediate growth,
commensurabilty and non-geometricity, Journal of Algebra, 272,
2004, 154-172
12. On isoperimetric profiles of finitely generated groups,
Geometriae Dedicata, 2003, v.100, 157-171.
11. Drift and entropy growth for random walks on groups, Annals
of Probability, v.31, n.3, 2003, 1193-1204.
10. Growth rates of small cancellation groups, Proceedings of the
workshop Random Walks and Geometry, Random walks and geometry, 421–430, Walter de Gruyter GmbH & Co. KG, Berlin, 2004.
9. On the geometry of infinite cyclic subgroups, Israel Journal of
Mathematics., v. 132, 2002, 373-380.
8. On growth rates of small cancellation groups, Functional Analysis. and
its Applications, 2002, v.36, no. 1, 93-95.
7. (with Iosif Polterovich), Explicit constructions of
universal R-trees and asymptotic geometry of hyperbolic spaces,
Bull. London Math. Soc. 33, 2001, no. 6, 727-734.
6. On the asymptotics of drift, Zapiski Nauchn. Sem. POMI, 2001,
T.283.
5. Drift and entropy growth for random walks on groups, Russian
Math. Surveys, 2001, T.57, v. 5, 179-180.
4. Instability of the virtual solvability and property of being
virtually torsion-free for quasi-isometric groups, IMRN, 21, 2000, 1097-1102.
3. Characteristics of the random walk on the wreath product of
groups, Zapiski Nauchn. Sem. POMI, 1999, T.256, 31-37.
2. An example of the drift, Russian Mathematical Surveys, 1999, T. 55,
no 5, 159-160.
1. (with Iosif Polterovich), Structures at infinity of
hyperbolic spaces, Russian Mathematical Surveys, T. 54, v.5, 1998.
Phd Thesis "Geometric and probabilistic properties of wreath products", 2001.
Habilitation Thesis "Geometric and probabilistic properties of amenable groups, 2012 pdf