Dapeng Zhan

 

Associate 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

 

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].

 

Professional Experiences

 

Associate Professor                     Michigan State University  2012 - present

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(κ;ρ) 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. (with Steffen Rohde) Backward SLE and Symmetry of Welding. Probability Theory and Related Fields, 164(3):815-863, 2016.

14. (with Mohammad A. Rezaei) Higher moments of the natural parameterization for SLE curves. Accepted by Ann. I. H. Poincare-Pr.

 

Preprints

 

1.    Decomposition of Schramm-Loewner evolution along its curve. In preprint, arXiv:1509.05015.

In this paper, it is proved that if one samples a point on an SLE curve using natural parametrization, then he sees a two-sided radial SLE near that point; and if one samples a point on the SLE curve using capacity parametrization, then he sees an SLE(κ,-8) curve near that point.

2.    (with Hao Wu) Boundary Arm Exponents for SLE. In preprint, arXiv:1606.05998.

In this paper, we derive boundary arm exponents for SLE. Combining with the convergence of critical lattice models to SLE, these exponents would give the alternating half-plane arm exponents for the corresponding lattice models.

3.    (with Mohammad A. Rezaei) Green's function for chordal SLE curves. In preprint, arXiv:1607.03840.

In this paper, we prove the existence of Green’s function for chordal SLE for any finite number of points, i.e., the rescaled probability that a chordal SLE curve (κ<8) passes through given points in the domain (expressed in terms of a limit), and provide the convergence rates and up to constant sharp bounds for these Green’s functions.

 

Teaching in Fall, 2016

 

MTH 428H: Honors Complex Analysis I [Course Website]

MTH 992-002: Random Variables and Stochastic Processes

Office hours: MWF: 11:15-12:15 or by appointment.