Joint colloquium of the probability and statistics workgroups
TU Darmstadt / Goethe-Universität Frankfurt / Gutenberg-Universität Mainz
Summer term 2022
On conditional propagation of chaos for interacting systems of neurons in a diffusive regime
The asymptotic speed of the maximal particle in on/off-Branching Brownian Motion
(Self-)interacting diffusions and sampling algorithms for rare event systems
July 1st, 2022, 15:15 Uhr, Rhein-Main-Kolloquium Stochastik, Goethe-Universität Frankfurt
Functional Representation Theorems for Exchangeable Laws
Functional Representation theorems (FRTs) for exchangeable random objects exist for many types of data structures, for example sequences (de Finetti/Hewitt-Savage),
partitions (Kingman), hierarchical structures, graphs or more general array-like data structures (Aldous-Hoover-Kallenberg). In this talk several known FRTs are presented and the language of category theory [vocabulary: cagegory, functor, natural transformation] is used to introduce an abstract concept of data structures, which allows for a unified formulation of many known FRTs. This leads to a conjecture about a "General FRT". No knowledge of category theory is assumed to follow this talk, the concepts will be motivated by statistical practise.
This research is funded by the DFG project 502386356.
16:15 Uhr Kaffeepause
At the edge of a cloud of Brownian particles
The talk concerns a model for the motion of particles carried in a turbulent fluid in which a single particle moves according to an SDE of the form dX_t= \sigma dB_t + dW(t,X_t). Here, W is a Gaussian field, describing the environment, and B is an independent Brownian motion representing some additional diffusivity. We are interested in the behaviour at large times, but far from the origin. There, we find a transition which is analogous to that between weak and strong disorder for polymer models, and at the transition the stochastic heat equation appears.
Ort: Robert-Mayer-Str. 10, Campus Bockenheim, Frankfurt/Main, Raum 711 gr.
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