Directed study - High dimensional probability

Mentor: Wai-Tong (Louis) Fan

Office: Rawles Hall 225

Email: waifan@iu dot edu

Meetings: Friday 2:30-4pm (Spring 2019)

Course description This is an independent study with guidance. Students will learn essential techniques and applications in high dimensional probability. Although the materials are ``discrete" probability, some general techniques can be routinely modified in the ``continuous settings".

Pre-requisites Students taking (or have taken) graduate level probability (M563 and M564 at IU). Basic knowledge about discrete-time Markov chains and continuous-time Markov chains (M463 and M464 at IU). Programming skills will be desirable but not necessary.

Expectation

• During each week, each student will present for about 30 mins and submit a type up in Latex. The type up can be about exercises assigned by the mentor.

• At the end of the course, each student will submit a final report to the mentor for grading. The report is an enhancement and organization of the weekly type up.

• This is a graduate course. Students are expected to be proactive and hard working, with access to guidance in study. Students are expected to keep on improving based on feedback.

Evaluation Course grades will be based on regular meetings and assignments, as well as the written report.

Logistics (Spring 2019)

• Weekly group meetings: ~1.5 hours (~30 mins presentation for each student)

• Dropbox: students will frequently type up their work (exercises assigned by the mentor) in Latex. Mentor will grade and give specific feedback to the write up.

• Students in the group are highly encouraged to meet among themselves to discuss and help each other.

Reading materials

• Reading assignments and exercises will from a combination of books and articles.

• We will start from Chapter 2 of the recent book ``High dimensional probability" by Roman Vershynin.

• http://www-personal.umich.edu/~romanv/papers/HDP-book/HDP-book.pdf

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Other resource

The following website provides some quick info about basic concepts in probability:

https://www.probabilitycourse.com/courses.php

For example, see Chapter 7 (Limit theorems and convergence of random variables).