**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.