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
Teaching
I am
teaching MATH 180B in Winter 2022.
Articles
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
.