Gregory F Lawler, A. Hollis Edens Professor

Please note: Gregory has left the Mathematics department at Duke University; some info here might not be up to date.

Contact Info:

Office Location:	121 Physics Bldg
Office Phone:	(919) 660-2800
Email Address:
Web Page:	http://www.math.duke.edu/~jose

Education:

B.A. 1976 University of Virginia M.A. 1977 Princeton University Ph.D. 1979 Princeton University

Research Interests: Probability and Statistical Physics

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.

Current Ph.D. Students   (Former Students)

• Michael Kozdron  
• Christian Benes  

Recent Publications   (More Publications)

1. Gregory F. Lawler, Oded Schramm, and Wendelin Werner, On the scaling limit of planar self-avoiding walk (Preprint, 0) [math.PR/0204277]
2. Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Values of Brownian intersection exponents I: half-plane exponents, Acta. Math. 187 (2001), 237--273 [math.PR/9911084]
3. Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Values of Brownian intersection exponents II: plane exponents, Acta Math. 187 (2001), 275--308 [math.PR/0003156]
4. Gregory F. Lawler, Oded Schramm, and Wendelin Werner, One-arm exponent for critical 2D percolation, Electronic J. of Probability, 7 (2002), paper no. 2 [~ejpecp]
5. Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Values of Brownian intersection exponents III: Two-sided exponents, Ann. Inst. Henri Poincare' 38 (2002), pp 109--123 [math.PR/0005294]