Helen (Guo-Ying) Lei

Helen (Guo-Ying) Lei, Postdoc
Department of Mathematics
California Institute of Technology

~~~ thshelen (at) gmail (dot) com ~~~

Papers

Hamiltonian ODE's on a Space of Deficient Measures, with L. Chayes and W. Gangbo.
On Convergence to SLE$_6$ I: Conformal Invariance for Certain Models of the Bond-Triangular Type and
On Convergence to SLE$_6$ II: Discrete Approximations and Extraction of Cardy's Formula for General Domains, with I. Binder and L. Chayes.
Journal of Statistical Physics 141, no. 2, 359-408 (2010).
Cardy's Formula for Certain Models of the Bond-Triangular Type, with L. Chayes.
Reviews in Mathematical Physics 19, no. 5, 511-565 (2007).
Random Cluster Models on the Triangular Lattice, with L. Chayes.
Journal of Statistical Physics 122, no. 4, 647-670 (2006).

Thesis: Critical Percolation, Universality, and SLE$_6$

Degenerate diffusion with a drift potential: a viscosity solutions approach, joint work with I. C. Kim, truncated version.

Talks

Hamiltonian ODEs on a space of deficient measures.
Viscosity Solution for Degenerate Diffusion With a Drift. (Warning: Fairly informal and contains mistakes/omissions.)
On Convergence to SLE$_6$.
Inhomogeneous Continuity Equation With Application to Hamiltonian ODE (v1) and script.
Convergence to SLE$_6$ for Percolation Models.
A Universality Result for Critical 2D Percolation. Click here for the abstract of L. Chayes' talk on the same subject.

Expository Writings

Notes on the first half of Otto's paper The Geometry of Dissipative Evolution Equations: The Porous Medium Equation (computation of the Hessian is incomplete).
Some material related to the numerical analysis qualifying exam.
Another write up of the random cluster expansion and Edwards-Sokal measure. This one contains an overabundance of details.
Some material related to the algebra qualifying exam.
A write up of the random cluster expansion.
Notes for my talk on domino tilings for Math 290K (Fall 2005).
Some (complex analysis) notes on Smirnov's paper.

Miscellaneous and Links