Stochastic Modeling

Preliminary meeting on April 23 at 1:00 pm (room tba)

In this seminar, we study selected topics in stochastic modeling, with a focus on the Kardar-Parisi-Zhang universality class. We mostly follows the survey of Corwin on KPZ Universality .

Possible topics include

1. Modeling of growth interfaces and the KPZ equation (Section 1 in KPZ Universality)

2. The Hopf-Cole Solution to the KPZ equation (Section 2 in KPZ Universality)

3. Stationary Solution to the open KPZ equation (Section 2 in Stationary distributions for KPZ)

4. Correspondence between the TASEP and last passage percolation (Section 1 in Lecture notes by Seppaläinen)

5. Introduction to Airy Processes (Sections 1-10-1.12 in Lecture notes by Quastel and Review by Ferrari)

6. Directed polymers and KPZ universality (Section 4 in KPZ Universality)

7. The PNG model (Section 2 in Lecture notes by Ferrari) [L.G.B.]

]Further topics will be announced if needed.

Once you have decided to participate in the seminar, you can reserve a specific topic via email to    dominik1.schmid (at) uni-a  (dot) de   (topics that have already been assigned are marked with name abbreviations). Otherwise, the topics will be assigned in a separate preliminary meeting.

Notes on the Seminar Procedure:

• In general, the basic lectures on probability provide sufficient prior knowledge. However, some presentation topics require additional knowledge, particularly in stochastic processes, combinatorics, and group theory. Relevant literature for self-study will be provided individually.

• Please schedule an individual meeting for preliminary discussion no later than two weeks before your presentation date. At this preliminary discussion, you are not required to have all the details of your presentation fully worked out, but a preliminary selection of topics for the presentation should already be made.

• The evaluation of the presentations will be announced once all participants have given their talks. However, you will receive individual feedback immediately after your presentation.

General Notes on Presentation Design:

• The presentation duration is a maximum of 60 minutes (including time for questions). It is recommended to design the presentation as a chalkboard lecture. Please practice your presentation in advance! Experience shows that a chalkboard presentation takes significantly more time than initially planned. In the case of paired presentations (Part I and II), please coordinate among yourselves regarding which aspects of the topic each of you will present.

• The presentation can be held either in German or English.

• Please remember that the presentation is aimed at your fellow students. Therefore, ensure that you address and engage your audience appropriately.

• The central evaluation criterion, in addition to the academic quality of the presentation, is the structure and design of the talk. Please focus on appropriate illustrations and visualizations of the presentation topics, using examples where possible! The recommended literature usually covers more topics than can be presented during the talk. Part of the presentation’s evaluation includes making an appropriate selection of results to present. You may also include proof sketches at suitable points.

• Please be prepared for questions to be asked during your presentation. This is in no way intended as criticism of your presentation! On the contrary, interested questions and a confident handling of audience inquiries demonstrate that you have thoroughly understood the topic.