Dapeng Zhan
Professor
Department of Mathematics,
Michigan State University
Office: C327
Wells Hall
Phone: 517-353-3838
Email: zhan@math.msu.edu
Education: Ph.D. California Institute of Technology, 2004
Teaching in Spring, 2020
MTH 992: Brownian motion and
stochastic analysis. [Notes, completed]
Teaching in Fall, 2019
MTH 320: Analysis I. [Website]
MTH 925: Random Variables and Stochastic Processes. [Notes] (completed).
Office hours: Mon: 2 每 3 pm, Tue: 9 每 10 am, Thu: 1 每 2 pm, or by email
appointment.
Teaching in Spring, 2019
MTH 992: Random Variables and Stochastic Processes, II. [Notes] (Completed).
Research Interests
Probability
Theory, Schramm-Loewner evolution (SLE), Statistical lattice models
Click
here to see my [CV].
Click
here to see my research statement [Research
Statement].
I gave
a lecture on Schramm-Loewner evolution. Click here to see the lecture notes [lecture]
Professional Experiences
Professor Michigan
State University 2017
- present
Associate
Professor Michigan
State University 2012
- 2017
Assistant
Professor Michigan
State University 2009
- 2012
Gibbs
Assistant Professor Yale
University 2007
- 2009
Morrey Assistant Professor UC
Berkeley 2004
- 2007
Awards and Grants
Simons
Fellowship (2016)
Salem Prize
(2012)
Sloan
Research Fellowship (2011-2015)
NSF
CAREER award: DMS
1056840 (2011-2018)
NSF
Grant: DMS
0963733 (2009-2013)
Publications
0. Random Loewner
Chains in Riemann Surfaces, PhD dissertation at Caltech, 2004.
1.
Stochastic Loewner evolution in doubly
connected domains, Probability
Theory and Related Fields, 129:340-380, 2004
2. Some
properties of annulus SLE. Electronic
Journal of Probability, 11:1069-1093, 2006.
3. The scaling
limits of planar LERW in finitely connected domains. Annals of Probability, 36(2):467-529,
2008.
4. Reversibility
of chordal SLE. Annals of
Probability, 36(4):1472-1494, 2008.
5. Duality of
chordal SLE. Inventiones
Mathematicae, 174(2):309-353, 2008.
6. Continuous
LERW started from interior points. Stochastic Processes and their Applications, 120:1267-1316, 2010.
7. Reversibility of some chordal SLE(百;老) traces. Journal of Statistical Physics,
139(6):1013-1032, 2010.
8. Duality of
chordal SLE, II. Ann. I. H.
Poincare-Pr., 46(3):740-759,
2010.
9. Loop-erasure
of planar Brownian motion. Communications
in Mathematical Physics, 133(3):709-720, 2011.
10. Restriction properties of annulus SLE. Journal
of Statistical Physics, 146(5):1026-1058, 2012.
11. Reversibility of
Whole-Plane SLE. Probability
Theory and Related Fields, 161(3):561-618, 2015.
12. Ergodicity of the tip of an SLE curve. Probability
Theory and Related Fields, 164(1):333-360, 2016.
13. Backward SLE and symmetry of welding. (with Steffen Rohde) Probability Theory and Related Fields,
164(3):815-863, 2016.
14. Higher moments of the natural parameterization for SLE
curves. (with
Mohammad A. Rezaei) Ann. I. H. Poincare-Pr., 53(1):182-199, 2017.
15. Boundary arm exponents for SLE. (with Hao Wu) Electronic
Journal of Probability, 22, Paper no. 89, 26 pp, 2017.
16. Green's function for chordal SLE curves. (with Mohammad A. Rezaei) To appear
in Probability Theory and Related Fields.
17. Decomposition of Schramm-Loewner evolution along its
curve. To appear in Stochastic
Processes and their Applications.
18. Decomposition of backward SLE in the capacity
parameterization. (with Benjamin Mackey) To appear in Stat. Probab. Lett.
19. Optimal Hölder continuity and dimension properties for
SLE with Minkowski content parametrization. To appear in Probability Theory and Related Fields.
20. Multipoint estimates for radial and whole-plane SLE. (with Benjamin Mackey) In preprint, to appear in
Journal of Statistical Physics.
Preprints
1. SLE
loop measures, arXiv:1702.08026, 2017.
2. Two-curve Green's function for $2$-SLE:
the interior case. In preprint, arXiv:1806.09663, 2018.
3. Two-curve Green's function for $2$-SLE: the
boundary case. In preprint, arXiv:1901.00254, 2019.
4. Time-reversal of multiple-force-point
SLE$_\kappa(\rho)$ with all force points lying on the same side, In
preprint, arXiv:1906.06005, 2019.