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| Gregory F. Lawler |
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| Adjunct Professor of Mathematics |
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Web Site Contact Information
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Education
Ph.D. (1979) Princeton University
Research Area: Probability, statistical physics
Most 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. Oded Schramm, Wendelin Werner, and I investigated the limit of lattice models in two dimensions that possess certain conformal invariance properties in the continuum limit. This project 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.
The big challenge for the future for these problems is understanding three dimensions.
Selected Publications
Intersections of Random Walks, Birkhäuser-Boston, 1991.
Values of Brownian intersection exponents I and II (with O. Schramm and W. Werner), Acta Mathematica 187 (2001), 237–273, 275–308.
Conformal restriction: the chordal case (with O. Schramm and W. Werner), JAMS 16 (2003), 917–955.
Brownian loop soup (with W. Werner), Probab. Theor. Rel. Fields 128 (2004), 565–588.
Conformally Invariant Processes in the Plane, American Mathematical Society, 2005.
Last modified: September 1, 2006