19th Probability Day Erlangen-München
- Organizers: Noam Berger (München), Andrej Depperschmidt ^{} (Erlangen), Nina Gantert (München), Andreas Greven ^{} (Erlangen), Markus Heydenreich (München), Gerhard Keller ^{} (Erlangen), Franz Merkl (München), Christoph Richard ^{} (Erlangen), Silke Rolles (München)
- The probability day takes place on Friday, May 15, 2020 via Zoom.
Speakers
- Margherita Disertori ^{} (Bonn): A model for liquid crystals in two and three dimensions.
Abstract: In 1949, L. Onsager proposed a statistical theory for a system of elongated molecules interacting via repulsive short-range forces. Onsager’s theory predicted the existence at intermediate densities of a nematic liquid crystal phase, in which the distribution of orientations of the particles is anisotropic, while the distribution of the particles in space is homogeneous and does not exhibit the periodic variation of densities that characterizes solid crystals (periodicity in all space dimensions).
I will introduce a toymodel for this problem consisting of long rods (in two dimensions) and anisotropic plates (in three dimensions). The rods/plates interact via purely hard core interactions and have a finite number of allowed orientations. For this model I will review some results and conjectures.
This is a joint work with A. Giuliani and I. Jauslin - Patrik Ferrari ^{} (Bonn): Time-time covariance for last passage percolation with generic initial profile
Abstract: We consider time correlation for KPZ growth in 1+1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In particular, this provides a rigorous proof of the exact formula of the covariance for the stationary case obtained in [SIGMA 12 (2016), 074]. Furthermore, we prove the universality of the first order correction when the two observation times are close and provide a rigorous bound of the error term. This result holds also for random initial profiles which are not necessarily stationary.
This is a joint work with Alessandra Occelli, Math. Phys. Anal. Geom. (2019), 22:1. - Xiaolin Zeng ^{} (Strasbourg): Local time of reinforced process and susy hyperbolic field.
Abstract: We start by review some classical theorems that relate local time of Markov jump processes and Gaussian free field. Then we introduced the vertex reinforced jump process, and its relation to the susy hyperbolic sigma field (aka $H^{2|2}$-field). A Bayes formula that allows one to relate GFF to the $H^{2|2}$-field will be discussed and, as application, we discussed an alternative proof of BFS-Dynkin isomorphisms discovered by Bauerschmidt, Helmuth and Swan. Joint work with Chang and Liu.
Program
- 14:15-15:15 Xiaolin Zeng
- 15:30-16:30 Patrik Ferrari
- 16:45-17:45 Margherita Disertori