Math @ Duke

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:
 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 selfavoiding 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)
 Gregory F. Lawler, Oded Schramm, and Wendelin Werner, On the scaling limit of planar selfavoiding walk
(Preprint, 0) [math.PR/0204277]
 Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Values of Brownian intersection exponents I: halfplane exponents,
Acta. Math. 187 (2001), 237273
[math.PR/9911084]
 Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Values of Brownian intersection exponents II: plane exponents,
Acta Math. 187 (2001), 275308
[math.PR/0003156]
 Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Onearm exponent for critical 2D percolation,
Electronic J. of Probability, 7 (2002), paper no. 2
[~ejpecp]
 Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Values of Brownian intersection exponents III: Twosided exponents,
Ann. Inst. Henri Poincare' 38 (2002), pp 109123
[math.PR/0005294]


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

