18.677 Stochastic Processes

18.677 Stochastic Processes


The class will start with a survey of key objects that arise in Integrable Probability and main types of results one proves about them. Students will be asked to pick their favorite topic and prepare a presentation (which would be required for a grade). The course will also feature outside lecturers giving survey and research talks related to the class.

The class meets on Tuesdays and Thursdays, 2:30-4 pm. 

Lectures will be automatically recorded. 

Lecture Notes (handwritten) 

Lecture Notes by Andrew Lin 

Outside lectures will be posted below, and are also available here.

02/25/2021. Speaker: Jimmy He (Stanford University)
Title: Limit theorems for descents of Mallows permutations. 
Abstract: The Mallows measure on the symmetric group gives a way to generate random permutations which are more likely to be sorted than not. There has been a lot of recent work to try and understand limiting properties of Mallows permutations. I'll discuss some work on the joint distribution of descents, a statistic counting the number of "drops" in a permutation, and descents in its inverse, generalizing work of Chatterjee and Diaconis, and Vatutin. The proof uses Stein's method with a size-bias coupling as well as a regenerative representation of Mallows permutations due to Gnedin and Olshanski.





Course Summary:

Date Details Due