Department of Mathematics

Dapeng Zhan

Picture of Dapeng Zhan

Professor

  • Ph.D., California Institute of Technology, 2004


Research Interests

My research interest focuses on the Schramm-Loewner evolution (SLE for short), which describes some random fractal curves in plane domains whose distribution is preserved under conformal (analytic and one-to-one) maps. It was introduced by Oded Schramm in 1999, who combined the Charles Loewner’s equation from Complex Analysis with a random input function. The merit of SLE is that one can now use the tools from Stochastic Analysis to analyze some random curves in the plane, which include the scaling limits of many two dimensional statistical physics models, e.g., critical site percolation, critical Ising models, Gaussian free field, loop-erased random walk, and uniform spanning tree. 

Selected Publications
  • Ergodicity of the tip of an SLE curve. Probab. Theory Rel., DOI: 10.1007/s00440-014-0613-5, 2015.  
  • (with Steffen Rohde) Backward SLE and the symmetry of the welding. Probab. Theory Rel., DOI: 10.1007/s00440-015-0620-1, 2015.  
  • Reversibility of whole-plane SLE. Probab. Theory Rel., DOI: 10.1007/s00440-014-0554-z, 2014  
  • Duality of chordal SLE, Invent. Math., 174(2):309-353, 2008.  
  • Reversibility of chordal SLE. Ann. Probab., 36(4):1472-1494, 2008.  
  • The scaling limits of planar LERW in finitely connected domains. Ann. Probab., 36(2):467-529, 2008.  
  • Stochastic Loewner evolution in doubly connected domains. Probab. Theory Rel., 129(3):340-380, 2004.