|Office Location:||121 Physics Bldg|
|Office Phone:||(919) 660-2800|
The bulk of my research is on random walk and Brownian motion, especially questions arising from statistical physics. A number of questions are inspired by a desire to understand self-avoiding random walk and other random walks with constraints.
Most of my work in the last few years has been in relating critical exponents such as the intersection exponent and disconnection exponent to fractal properties of Brownian motion. In particular it has been shown that the Hausdorff dimension of the set of cut points for Brownian motion in two and three dimensions and the Hausdorff dimension of the outer boundary of planar Brownian motion can be described in terms of these exponents.
Recently, I have been working with Oded Schramm and Wendelin Werner investigating the limit of lattice models that possess certain conformal invariance properties in the continuum limit. This project has been produced a number of results, e.g., we have verified a conjecture of Mandelbrot that the Hausdorff dimension of the outer boundary of planar Brownian motion is 4/3.