Jan Swart - Teaching

Themes for theses:

Periodic behaviour of an interacting particle system (diplom thesis)

Cooperative branching in a random environment (diplom thesis)

Sticky Brownian motions (diplom thesis)

List of available themes for PhD theses

Future lecture:

In the summer semester 2025, I will offer the course Quantum Probability Theory. We will use these lecture notes.

Past lectures:

Interacting particle systems

I have taught Interacting Particle Systems in the Seminar on Probability 2 during the winter semesters 2024, 2021, 2019, and 2015, and as the subject NMTP612 in 2011 and 2009. Here is the final version of the lecture notes. Here are versions of the lecture notes from September 13, 2022, October 9, 2024, October 10, 2024, October 14, 2024, January 6, 2022, September 22, 2021, November 1, 2021, November 3, 2021, and December 10, 2021, October 2, 2019, October 23, 2019, November 15, 2019, November 18, 2019, November 25, 2019, December 4, 2019, and December 16, 2019, April 7, 2017, June 29, 2011 and 2009.

The lecture notes are also available on arXiv:1703.10007.

Here is a collection of programs that you can use to simulate your own favourite interacting particle system, and make a colorful picture of it. For a few special systems you can also use this nice applet.

I taught a minicourse about interacting particle systems during the Workshop YEP XVII: "Interacting Particle Systems" (Aug 30 - Sep 3, 2021). Here you can find my slides and more.

Random Matrix Theory

In the summer semester 2024, I have taught the Specialized seminar in probability and mathematical statistics. The theme was Random matrices and we used the book Topics in random matrix theory by Terence Tao. Here are some additional notes which include the introductory lecture as well as notes on Section 2.4.1 of the book. Here are notes on free independence.

In the winter semester 2017/2018 I taught the same material in the Seminar on Probability for Ph.D. Students I - NMTP613, which took place on Tuesdays 14-15:30. Here is an older version of the Notes on Free Independence that I wrote for the seminar.

Advanced Markov Chains

In the fall semester 2023/24 I have taught the Seminar on Probability 2. The theme was Advanced Markov Chains. Here is the final version of the lecture notes, with minor additions and corrections compared to the first, second, third, and fourth, fifth, sixth, seventh, and eighth versions.

In the summer semester 2018 I taught the same material in the course Advanced Markov Chains - NMTP566. Here are the lecture notes. Here are the first, second, third, fourth, fifth, and sixth version. Here are the exam of May 24 and the exam of July 9, with solutions. Here are Lecture notes from 2012 from a similar course, with the Exam of May 16th, 2012, with solutions.

Large Deviations

In the summer semester 2023, together with Jan Seidler, I have been teaching the Specialized seminar in probability and mathematical statistics. The theme was Large deviations. Here is present version of the lecture notes. Here are the first, second, third, fourth, and fifth versions.

Taught perviously during the spring semester of 2021 in the Specialized seminar in probability and mathematical statistics. Here is the last version of lecture notes. (Here are the older first, second, third, fourth, fifth, sixth, seventh and eighth versions.) Here are slides for Chapter 0 and Section 3.2.

Taught previously in the autumn/winter of 2016/17 in the "Advanced topics of the field" at the Department of Probability and Mathematical Statistics, MFF, Charles University. I am using these lecture notes. (Here are the first, second, third, fourth, fifth, sixth, and seventh version of the lecture notes.) Here is the exam. Here are the even older Lecture notes January 10th, 2012. These were used for the course Advanced topics from probability, statistics and random processes I - NSTP029 at Charles University, Prague, fall 2011.

The Brownian web and net

During April 2023, I have been teaching a guest lecture in the Applied and Theoretical Mathematics master program at Paris Dauphine-PSL. The theme was The Brownian web and net. Here is a present version of the lecture notes. (Here are the first and second version.) The lectures took place at ENS and the schedule was as follows:

Wednesday April 5 14:00-17:00 ENS salle Cartan
Thursday April 6 9:00-12:00 ENS salle W
Wednesday April 12 14:00-17:00 ENS salle Cartan
Thursday April 13 9:00-12:00 ENS salle W
Wednesday April 19 14:00-17:00 ENS salle Cartan
Thursday April 20 9:00-12:00 ENS salle W

Markov Chains and Mixing Times

In the fall semester 2022/23 I have taught the Seminar on Probability 2. The theme is Mixing times of Markov chains using the lecture notes of Justin Salez, available here, as well as his article Cutoff for non-negatively curved Markov chains. Here is the latest version of the additional lecture notes. (Here are the first and second versions.)

In the fall of 2020 I have taught the Seminar on Probability 2 using the book David A. Levin, Yuval Peres, and Elizabeth Wilmer: Markov Chains and Mixing Times. The seminar takes place each Thursday from 15:40-17:10. Here are slides of the first lecture and the final lecture. Here is a short note on Gibbs measures.

Brownian continuum objects

During the summer semester 2022 I have taught the Specialized seminar in probability and mathematical statistics. The theme was Brownian continuum objects: the excursion, tree, snake, map, web, net, and castle. Here is the present version of the lecture notes. Here are the first, second, third, fourth, fifth, sixth, seventh, eighth, and ninth version.

Quantum Probability Theory

In the summer semester 2020 I have taught Quantum Probability Theory at the Department of Probability and Mathematical Statistics, MFF, Charles University. Here are the lecture notes (fourth version of 27.4.2020). Here are the first and second and third version.

Here are the exams of June 2nd, 2020, June 30th, 2017, July 4th, 2017, and September 5th, 2017, with answers. Time for these exams was 3 hours. Exercises 2 (d) and 3 (d) of the exam of Sept. 5, 2017 are quite hard; in particular, a complete solution to Ex. 2 (d) cannot be expected within the time frame of the exam.

Here are the lecture notes of 2017. Here are the Lecture notes from 2013. Here are the Lecture notes from 2010. Here are the Lecture notes from 2007. Here is a Summary of Chapter 5. Here are the Exam of June 20, 2013, with solutions, Exam of June 25, 2008, Exam of September 18, 2008, with solutions, Exam of September 30, 2008, with solutions. Here is the Exam of June 22, 2007, with solutions. Here are Lecture notes from 2004 from a similar course taught at Erlangen University.

Random Graphs and Complex Networks

Taught in the summer semester 2019 in the Specialized seminar in probability and mathematical statistics. Based on the books Random Graphs and Complex Networks by Remco van der Hofstad. Here are notes from February 27th and April 17th.

Spatial Models in Population Biology

Here are the slides for my lectures at the Summer School Probabilistic Structures in Evolution, June 2018, on the Reisensburg, Günzburg, Germany. Due to a lack of time, only the first three lectures have been presented.

Probability on Graphs

A seminar on Geoffrey Grimmett's book Probability on Graphs, taught in the summer semester 2016 in the Seminar on Probability for Ph.D. Students II at the Department of Probability and Mathematical Statistics, MFF, Charles University. Here are slides about the Uniform Spanning Tree.