Greg Lawler, 128B Physics Bldg, Thursdays 1:30-3:30, and by appointment
Bass, Probabilistic Techniques in Analysis
Lawler, Intersections of Random Walks
The first half of the course will cover material that generally goes under the name of ``potential theory'' or study of the Laplacian. We will simultaneously do potential theory in both continuous and discrete d-dimensional space. We will also consider somewhat the case of arbitrary graphs. We will use probabilistic tecniques as well as other techniques; this will require a quick introduction to Brownian motion in the beginning of the course. The material on continuous potential theory can be found in the first two chapters of Bass. For the discrete case, the first two chapters of Lawler will be the main reference. The latter part of the course will deal with more advanced topics in the interplay of PDE, probability theory, and complex analysis. The latter chapters of Bass will be used for much of this part of the course, although we will have to choose only a few topics to discuss. A few weeks late in the course, if student interests warrants, will be devoted to the relationship between the Laplacian and Brownian motion on manifolds.
Lecture Notes will be available on reserve in the math-physics library.
Exercises in postscript
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Last modified: 5 September 96