### Online: August 4 – 5, 2020

*Organizer*: Amir Dembo

Many-body random systems are of fundamental importance in statistical mechanics. They model diverse phenomena, such as phase transitions, turbulent fluids or even traffic flow. Probabilists seek to answer central questions concerning such systems, selecting and analysing models that are simple enough that they may be analysed in a rigorous mathematical fashion, yet rich enough to capture important physical features. A guiding theme is universality: discovering and analysing mathematical structures that describe basic shared aspects of seemingly very different natural phenomena.

Plenary speaker: Ofer Zeitouni, Weizmann Institute of Science

**Session speakers:**

- Sourav Chatterjee. Stanford University, USA
- Amir Dembo, Stanford University
- Daniel Remenik, University of Chile
- Lisa Sauermann, Stanford University
- Insuk Seo, Seoul National University, South Korea

**Schedule:**

15:00 – 16:10 UTC, Aug 4 | Ofer Zeitouni (plenary) |

16:20 – 17:10 | Amir Dembo |

17:20 – 18:10 |
Daniel Remenik |

00:20 – 01:10 UTC, Aug 5 | Sourav Chatterjee |

01:20 – 02:10 | Lisa Sauermann |

02:20 – 03:10 | Insuk Seo |

### Non-intersecting Brownian motions with outliers, KPZ fluctuations and random matrices

**Daniel Remenik**

A well known result implies that the rescaled maximal height of a system of N non-intersecting Brownian bridges starting and ending at the origin converges, as N goes to infinity, to the Tracy-Widom GOE random variable from random matrix theory. In this talk I will focus on the same question in case where the top m paths start and end at arbitrary locations. I will present several related results about the distribution of the limiting maximal height for this system, which provides a deformation of the Tracy-Widom GOE distribution: it can be expressed through a Fredholm determinant formula and in terms of Painlevé transcendents; it is connected with the fluctuations of models in the KPZ universality class with a particular initial condition; and it is connected with two PDEs, the KdV equation and an equation derived by Bloemendal and Virag for spiked random matrices. Based on joint work with Karl Liechty and Gia Bao Nguyen.

## Pacific Rim Conference on Mathematics

The Eighth Pacific Rim Conference on Mathematics will be held at online from Monday 3th August to Tuesday 11th August 2020. Originally conceived as meeting at U.C. Berkeley in the same week, the conference will now take place in a virtual format. The PRCM will be a high profile mathematical event that will cover a wide range of exciting research in contemporary mathematics. Its objectives are to offer a venue for the presentation to and discussion among a wide audience of the latest trends in mathematical research, and to strength ties between mathematicians working in the Pacific Rim region. The conference will provide junior researchers with opportunities to engage and collaborate with established colleagues within and between the many represented mathematical disciplines.

Date of closure: Aug 05, 2020

Venue: Live-streamed online

Posted on Jul 31, 2020 in Events, Workshops & Congresses