Math 623- Advanced Probability (Fall 2009)

Instructor: Xia Chen

Office: Temple 106, 974-4284.

Email: xchen@math.utk.edu

Website: http://www.math.utk.edu/~xchen

Office Hours: MWF 1:30p.m -2:20 p.m.

Class: MWF 2:30 p.m- 3:20 p.m EPS (Earth and Planetary Science) 413.

Text book:
Random walk intersections: large deviations and related topics. (This is a newly completed monorgraph written by the instructor, and will be soon published by Mathematical Survey and Monorgraphy, American Mathematical Society)

Reference Books:

1. Dembo, A. and Zeitouni, O. (1998). Large Deviations Techniques and Applications. (2nd ed. Springer, New York.
2. Le Gall, J-F. (1990). Some properties of planar Brownian motion. Lecture Notes in Math. {\bf 1527} 111-235, Springer, Berlin.

   Course Description:
   Quantities measuring the amount of self-intersection of a random path, or of mutual intersection of several independent random paths have been studied extensively for nearly twenty years. This research is often motivated by the role these quantities playing in renormalization group methods for quantum field theory, random plymers and other models in physics. In recent years, some substantial progresses have been made in the large deviations for the intersection local times and related quantities which acomponies with new technologies, opens new frontiers and raises new problems in this areas. This course is designed to learn some of the new developments in this area. The topic of this course is "Large deviations in sample path intersections".

   Grading policy:
   There will be no test and exams. Your performance in the classroom and in homework will decide the grade you receive.

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