The topics of this course change each semester, and multiple sections may be offered. Advanced topics in probability offered according to students demand and faculty availability.

This course introduces probabilistic models in which large-dimensional stochastic systems can be analyzed exactly using algebraic techniques. Principal examples arise in two-dimensional statistical mechanics, including random tilings, last passage percolation, six-vertex model, interacting particle systems, and random matrices. On the methods side, we will do many computations in the algebra of symmetric polynomials, learn about determinantal point processes, and use of difference operators in the asymptotic analysis.

Prerequisites: basics of probability theory, linear algebra, and complex analysis. Experience with rigorous mathematical proofs.

Undergraduates who would like to take the class, must attend the first lecture. After the lecture, they can contact the instructor for the enrollment code.

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