This term, all seminars take place Thursdays at 2pm, room B3.03 (Zeeman Building), unless indicated otherwise.

Schedule for

Agelos Georgakopoulos, 11.01.2018


03.10.2019 Chiranjib Mukherjee (Münster)
The KPZ equation in $dgeq 3$ and the Gaussian multiplicative chaos in the Wiener space
In the classical finite-dimensional setting, Gaussian multiplicative chaos (GMC) is obtained by tilting an ambient measure by the exponential of a centred Gaussian field indexed by a domain in the Euclidean space. In the two-dimensional setting and when the underlying field is "log-correlated", GMC measures share a close connection to the 2D Liouville quantum gravity, which has seen a lot of revived interest in the recent years. A natural question is to construct a GMC in the infinite-dimensional setting, where techniques based on log-correlated fields infinite dimensions are no longer available. In the present context, we consider a GMC on the classical Wiener space, driven by a (mollified) Gaussian space-time white noise. In $dgeq 3$, in a previous work with A. Shamov and O. Zeitouni, we have showed that the total mass of this GMC, which is directly connected to the (smoothened) Kardar-Parisi-Zhang equation in $dgeq 3$, converges for small noise intensity to a well-defined strictly positive random variable, while for larger intensity (i.e. for small temperature) it collapses to zero. For the weak disorder case, we have also studied in a series of works with F. Comets (Paris) and C. Cosco (Paris), the properties of the above random limit and its space-time fluctuations. For the strong disorder case, we will also report on joint work with Y. Bröker (Münster) where we study the endpoint distribution of a Brownian path under the GMC measure in this setup and show that, for low temperature (i.e., strong disorder), the endpoint GMC distribution localizes in few spatial islands and produces only asymptotically purely atomic states.
Contact: Stefan A
10.10.2019 Alexander Sodin (Queen Mary University)
A decorated version of the Airy point process, and the stochastic heat equation
Approximately 10 years ago, special solutions to the stochastic heat equation were found to be related to the stochastic processes of random matrix theory. We interpret one of these results as an identity in distribution. Based on joint work with Vadim Gorin.
Contact: Nikos
17.10.2019 Monia Capanna (Buenos Aires)
Hydrodynamic limit and fluctuations for a mean field opinion model
In this talk I analyze the dynamics of an opinion model in a population of N agents with mean field interaction. Every agent is endowed with an opinion on [0,1] which is updated at a rate determined by the average opinion of the population. We study the hydrodynamic behaviour of the model with two different time scales. First we prove that, when the system is accelerated by the factor N^1/2, the average opinion remains constant and the agents tend to reach the consensus state. After we show that, under the time scale N^2, the average opinion feels the effect of the fluctuations and evolves as a Wright Fisher diffusion. Furthermore, if we zoom in on the drifting average, we see that the individual opinions are distributed according to the invariant measure of a Ornstein Uhlenbeck process with parameter depending on the position of the average opinion. This is a joint work with I. Armendariz, C. da Costa and P. Ferrari.
Contact: Stefan G



14.11.2019 Jakob Björnberg (University of Gothenburg)
Random permutations and Heisenberg models
We discuss probabilistic representations of certain quantum spin systems, including the ferromagnetic Heisenberg model, in terms of random permutations. The cycle structure of the random permutations is connected with the correlation structure in the spin-system, and it is expected that this cycle structure converges to a distribution known as Poisson-Dirichlet, in the limit of large systems. This problem is open but we present some partial progress.
Contact: Daniel
21.11.2019 Alexei Bufetov (University of Bonn)
Random tilings and representations of classical Lie groups
Asymptotic representation theory deals with questions of probabilistic flavor about representations of groups of growing size. For classical Lie groups there are two distinguished regimes of growth. One of them is related to representations of infinite-dimensional groups, and the other appears in random tilings problems. In the talk I will discuss differences and similarities between these two settings.
Contact: Oleg

05.12.2019 Michał Kotowski (University of Warsaw)

Contact: Peter M.