Winter Semester 2020 (-2021)
The seminar is devoted to the study of Multispecies Interacting Particle Systems, most importantly, multispecies Asymmetric Simple Exclusion Process. The study of such stochastic systems leads to many nice phenomena and also is motivated by connections to Mathematical Physics, Algebra, and Combinatorics. The goal of the seminar is to provide an introduction to this research field.
The first meeting will be via zoom on 16 July, 13:00 . Please write me an email if you wish to participate in the first meeting ( Please use your uni-bonn address. I will send you a link to zoom in a reply email. My email is alexey DOT bufetov AT gmail DOT com or you can find uni-bonn email on the university website.)
The list below consists of references to the research literature from the last 30 years. I believe that the field is quite accessible for beginners and that this will not create any major difficulties; we will cover only part of results from those papers.
Possible Topics:
0) Basic definitions: asymmetric simple exclusion process, second class particles, review of some known results (probably will be done by me as the first talk).
1) P.A. Ferrari, C. Kipnis, Second class particles in the rarefaction fan , http://www.numdam.org/item/AIHPB_1995__31_1_143_0/
2) TASEP, second class particle, and last-passage percolation. Pablo A. Ferrari, Leandro P. R. Pimentel , Competition interfaces and second class particles https://arxiv.org/abs/math/0406333
3) P.A. Ferrari, J. Martin, Stationary distributions of multi-type totally asymmetric exclusion processes , https://arxiv.org/abs/math/0501291
4) Omer Angel, Alexander Holroyd, Dan Romik , The oriented swap process , https://arxiv.org/abs/0806.2222
5) Gideon Amir, Omer Angel, Benedek Valkó The TASEP speed process , https://arxiv.org/abs/0811.3706
6) P.A. Ferrari, P. Goncalves, J. Martin, Collision probabilities in the rarefaction fan of asymmetric exclusion processes, https://arxiv.org/abs/0804.1770
7) A. Ayyer, S. Linusson, Correlations in the Multispecies TASEP and a Conjecture by Lam , https://arxiv.org/abs/1404.6679
8) Omer Angel, Alexander E. Holroyd, Dan Romik, Balint Virag , Random Sorting Networks, https://arxiv.org/abs/math/0609538