Spring 2012: MAT 235C - Probability Theory

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Course Information

• Instructor: Dan Romik
• Lectures: T 3:00-4:30, R 2:40-4:00 in Bainer 1130
• Discussion section: None
• Office hours: By appointment (or drop by MSB 2218)

Overview

This was the third quarter of a three-quarter graduate probability theory sequence (235A/B/C) taught during the 2011-2012 academic year. The 235C course had two parts: selected topics from the last chapter of Durrett's book (Brownian motion), followed by an introduction to percolation theory and related discrete planar processes such as the self-avoiding random walk. The percolation material covered classic theory as well as exciting developments from the previous 10 years, recognized in two Fields Medal award decisions.

Textbook

Probability: Theory and Examples (4th Ed.) by Rick Durrett (Chapter 8). Additional references: Percolation (2nd Ed.) by Geoffrey Grimmett (Chapters 1-2) and Lectures on two-dimensional critical percolation by Wendelin Werner (Chapters 1-2).

Prerequisites

Undergraduate classes in probability and real analysis, equivalent to UC Davis Math 125 and Math 135.

Grading

A final project consisting of reading a research paper or section of a book and writing about it. Depending on the number of participants, students may have been required to present their project in a short (25-30 minute) lecture.

Recommended Reading

• Probability with Martingales by David Williams
• An Introduction to Probability Theory and Its Applications, Vols. 1-2 by William Feller
• Percolation (2nd Ed.) by Geoffrey Grimmett