Graduate Seminar S4F6 WS 2024/25:

Branching Brownian Motion and Related Processes

Prof. Dr. Anton Bovier 

Time and place: Tuesdays, 16h ct in Room 0.011

 

The analysis of extreme values of stochastic processes has for a long time been an important theme of applied probability. While much of the classical theory concerned independent random variables or the identification of conditions under which the extremes of a processs are well described by those of iid variables, more recently, a class of processes where correlations just begin to matter has emerged as a new universality class. They are called log-correlated processes since the covariance decays essentially like the logarithm of the  distance. The classical example of such a process is Branching Brownian Motion (BBM) and its close relative, the Branching Random Walk (BRW). In these examples, the underlying tree structure helps in the precise anlysis of the laws of the maxxima and the extremal process. But many examples without expleicit trees structure have been shown to fall in the same class: the Gaussian Free Field (GFF), cover times of random walks, and, quite curiously, certain features of the properties of the (randomised) Riemann zeta fuction on the critical line. In the seminar we will focus on branching Brownian motion and the analysis of its extreme values, but according to interest, some related processes can also be discussed.

Literature:

Anton Bovier, Extreme values of random processes, Lecture Notes.

Anton Bovier, Gaussian processes on trees. Cambridge University Press, 2016.

Marek Biskup. Extrema of the two-dimensional Discrete Gaussian Free Field. Lecture Notes, 2017

Louis-Pierre Arguin, Extrema of log-correlated random variables: Principles and Examples, https://arxiv.org/abs/1601.00582, 2016.

 

Note that I will be back in Bonn only on July 15. There will be a

Preparatory meeting on Tuesday, July 16 in my office.

If you are interested in the seminar, please send me an email before.