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.
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.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.
Here is an updated version of the lecture notes of September 13th, 2022.
During the winter semester 2021 I have taught Interacting Particle Systems in the Seminar on Probability 2. Here are the lecture notes and here are the first, second, third, and fourth version. 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.
I taught this subject earlier in the Seminar on Probability 2 (Fall 2019). Here are versions of the lecture notes from October 2, October 23, November 15, November 18, November 25, December 4, and December 16. Here are the slides of the first lecture.
Before this, I taught the subject in the Seminar on Probability 2 (autumn/winter of 2015/16). Here are the lecture notes (version of 7.4.2017). Here are the slides of the first lecture. Here are lecture notes from June 29, 2011 and lecture notes from 2009. These were for the course NSTP190 at Charles University.
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.