Tianyi Zheng


I am an Associate Professor in the Department of Mathematics at the UC San Diego. Before coming to UCSD in the Fall of 2016, I was a postdoc in the Department of Mathematics at Stanford University. I received Ph.D. in Mathematics from Cornell University in 2013.


My primary research interest is in random walks on groups. I'm also interested in harmonic functions on groups, groups of intermediate volume growth and subgroup dynamics in the Chabauty spaces.


Here is my CV.



Email: tzheng2 AT math.ucsd.edu

Office: 6202 Applied Physics and Mathematics, UCSD




I am teaching MATH 180B in Winter 2022.






o   Asymptotic behaviors of random walks on countable groups. Survey article submitted to the Proceedings of ICM 2022. PDF.


o   Law of large numbers for the drift of two-dimensional wreath product. with Anna Erschler, accepted for publication in Probab. Theory Related Fields, arXiv: 2011.07628 (2020).


o   Isoperimetric profiles and random walks on some groups defined by piecewise actions.  With L. Saloff-Coste, accepted for publication in Probab. Theory Related Fields. (2021).


o   Speed of random walks, isoperimetry and compression of finitely generated groups. With J. Brieussel, Ann. of Math. (2) 193 (2021), no. 1, 1–105.


o   Random walks on discrete affine groups. With J. Brieussel and R. Tanaka, accepted for publication in Groups Geom. Dyn. (2021).


o   On FC-central extensions of groups of intermediate growth,

submitted (2020), arXiv 2001.07814



o   Neretin groups admit no non-trivial invariant random subgroups,

submitted (2019), arXiv 1905.07605.



o   On rigid stabilizers and invariant random subgroups of groups of homeomorphisms,

submitted (2019), arXiv 1901.04428.



o   Growth of periodic Grigorchuk groups,

         with Anna Erschler. Invent. Math. 219 (2020), no.3, 1069-1155.  arXiv 1802.09077.


o   Isoperimetric inequalities, shape of F{\o}lner sets and groups with Shalomճ property H_FD,

         with Anna Erschler. to appear in Ann. Inst. Fourier (Grenoble) (2017), arxiv 1708.04730.



o   Shalom’s  property H_FD and extensions by \mathbb{Z} of locally finite groups,

          with Jrmie Brieussel. Israel J. Math, (2018), arxiv 1706.00707.



o   Random walks among time increasing conductances: heat kernel estimates,

          with Amir Dembo and Ruojun Huang. Probab. Theory Relat. Fields, (2018), arxiv 1705.07534.


o   On groups, slow heat kernel decay yields Liouville property and sharp entropy bounds,

          with Yuval Peres. Int. Math. Res. Notices, rny034, (2018) arXiv 1609.05174.


o   Infinitely supported Liouville measures of Schreier graphs,

          with Kate Juschenko. Group Geom. Dyn, 12, (2018), no.3  arXiv 1608.03554 .


o   Isoperimetric profiles and random walks on some permutation wreath products

          with Laurent Saloff-Coste. Revista Matematica Iberoamericana, 34 (2018), no.2  arXiv 1510.08830 .


o   Random walks and isoperimetric profiles under moment conditions,

           with Laurent Saloff-Coste. Ann. Probab. 44 (2016), no.6 arXiv 1501.05929 .


o   Random walks on free solvable groups,

         with Laurent Saloff-Coste. Mathematische Zeitschrift, 279(3-4), 811-848. pdf .


o   Random walks on nilpotent groups driven by measures supported on powers of generators,

          with Laurent Saloff-Coste Groups, Geom. Dyn, 9 (2015), no. 4 arXiv 1211.3003 .


o   Random walks under slowly varying moment conditions on groups of polynomial volume growth,

           with Laurent Saloff-Coste Proceedings of the Conference "Talking across Fields",

           Annales de la Faculte des Sciences de Toulouse. arXiv 1507.03551 .


o   Large deviations for stable like random walks on Z^d with applications to random walks on wreath products,

            with Laurent Saloff-Coste. Electronic Journal of Probability, Vol.18, no.93.


o   On some random walks driven by spread-out measures measures,

            with Laurent Saloff-Coste. "Groups, graphs and random walks" 444д74, 

                     London Math. Soc. Lecture Note Ser., 436, Cambridge Univ. Press, Cambridge, 2017.



 Past teaching at UCSD


MATH180A Winter 2017

MATH180C Spring 2017

MATH289A Spring 2017

MATH280A Fall 2017

MATH280B Winter 2018

MATH280C Spring 2018