Zhongyang Li

I am a postdoc research fellow in Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge. My host is Prof. Geoffrey Grimmett.
I finished my Ph.D. in 2011 from the Department of Mathematics at Brown University. My advisor was Prof. Richard Kenyon.
Before coming to Brown, I was an undergraduate student in Fudan University (2002-2006).
I am interested in probability theory and statistical physics.

Publications and Preprints:

1. Local statistics of realizable vertex models, Commun.Math.Phys, 304, 723-763(2011), arxiv
2. Spectral curve of periodic Fisher graphs, accepted upon revision , J.Stat.Phys. arxiv
3. Critical temperature of periodic Ising models, Commun.Math.Phys, 315, 337-381(2012), arxiv
4. 1-2 model, dimers, and clusters, Electron.J.Probab., pdf
5. Self-avoiding walks and the Fisher transformation, with Geoffrey Grimmett, Electron.J.Combin., arxiv
6. Uniqueness of infinite homogeneous clusters in 1-2 model, submitted, arxiv
7. Bounds on connective constants of regular graphs, with Geoffrey Grimmett, Combinatorica, arxiv
8. Strict inequalities for connective constants of transitive graphs, with Geoffrey Grimmett, submitted, arxiv
9. Counting self-avoiding walks, with Geoffrey Grimmett, submitted, arxiv
10. Conformal invariance of isoradial dimers, submitted, pdf
11. Locality of the connective constant on Cayley graphs, submitted, pdf

Teaching:

• Lattice Models in Probability and Statistical Mechanics Description
  Michaelmas 2012, Tuesdays, 12pm-1pm, MR11
  Lecture 1: Introduction, Dimer Model; Read Section 1.1, Section 3 of arxiv:0910.3129
  Lecture 2: Height function; Read Section 2 of arxiv: 0910.3129
  Lecture 3: Torus graph; Read Section 4.2 of arxiv: 0910.3129
  Lecture 4: Partition function, free energy; Read Section 4.5 of arxiv: 0910.3129
  Lecture 5: Local statistics; Secion 3 of arxiv:math/0105054
  Lecture 6: Convergence of the free energy, Read Section 7 of arxiv:math/0008220
  Lecture 7: Ising model and Fisher correspondence, Read Section 3 of arxiv:1008.3934
  Lecture 8: Duality transformation, Dimer model on non-bipartite graphs, Read Section 3 of arxiv:1008.3934
• Introductory Calculus 1
  Fall 2010, MWF 9am-10am, Brown University
  
• Introductory Calculus 2
  Fall 2009, MWF 10am-11am, Brown University