Spring 2025, Probability Topics: A Walk in the Random Park

Instructor: Jacob Richey

Course details:

Thursday 16:15-17:45, BME Building H Room H406. Neptun code BMETESZMsMVFVA-00

Suggested texts

Syllabus

This course will focus on three models: random walks, percolation, and first passage percolation.
For each topic, we will start by reviewing classical results and methods, and then move on to recent ideas and papers.

Papers for presentation

Here are the papers I suggest for presentations. Your presentation should consist roughly of two parts: describing the general structure of the paper or or of one of its theorems (~5-10 minutes), and a deep dive into a proof of one lemma or fact (~20-25 minutes).

Schedule
Date Topics Relevant text Suggested exercises
Feb 13 Random walk basics: LLN, CLT, LCLT D Theorem 3.5.2 (HE) Exercises 1.8, 1.9; (RW) Exercises 1.4, 1.7, 2.7, 2.9
Feb 20 LCLT, Green's function, boundary problems, capacity D Theorem 3.5.2, RW Chapter 4