Rhein-Main Kolloquium Stochastik

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Gemeinsames Kolloquium der Arbeitsgruppen Stochastik

TU Darmstadt / Goethe-Universität Frankfurt / Gutenberg-Universität Mainz

 

Termine im Wintersemester 2017/2018

 

Freitag, 19.01.2018

Universität Mainz, Institut für Mathematik, Staudingerweg 9, Raum 05-432 (Hilbertraum):

15:15 Uhr: Steffen Dereich (Münster): Extended notions of local convergence for sequences of random graphs

Local convergence also known as Benjamini-Schramm convergence is an analogue of the Palm measure concept for growing sequences of finite random graphs $(G_n)_{n\in\mathbb N}$. Here one centers the graph around a uniformly chosen vertex and considers distributional convergence (in an appropriate local sense) to a random rooted and connected graph $(G,o)$  (in most cases a tree). At least on an informal level the local limit provides many insights about the structure of large graphs. For instance, the relative size of the largest component typically converges in probability to the probability that the graph $G$ is infinite.

In this talk we introduce new extended notions of local convergence that incorporate additional information on the graph localised around a uniformly chosen vertex. In one variant we keep information on the shortest weight-path to a second uniformly chosen vertex which can be interpreted as the path along which an infection occurs. A second variant keeps track of the local visits of a random walk run on the random graph.

 

16:45 Uhr: Peter Mörters (Köln): Metastability of the contact process on evolving scale-free networks

We study the contact process in the regime of small infection rates on scale-free networks evolving by stationary dynamics. A parameter allows us to interpolate between slow (static) and fast (mean-field) network dynamics. For two paradigmatic classes of networks we investigate transitions between phases of fast and slow extinction and in the latter case we analyse the density of infected vertices in the metastable state.

This is joint work with Emmanuel Jacob (ENS Lyon) and Amitai Linker (Universidad de Chile).

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Freitag, 26.01.2018

Universität Frankfurt, Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711 (groß):

15:15 Uhr: Wolfgang König (WIAS / TU Berlin): The principal part of the spectrum of random Schrödinger operators in large boxes

We consider random Schr\"odinger operators of the form $\Delta+\xi$, where $\Delta$ is the lattice Laplacian on $\mathbb Z^d$ and $\xi$ is an i.i.d. random field, and study the extreme order statistics of the eigenvalues for this operator restricted to large but finite subsets of $\mathbb Z^d$. We show that, for $\xi$ with a doubly-exponential type of upper tail, the upper extreme order statistics of the eigenvalues falls into the Gumbel max-order class, and the corresponding eigenfunctions are exponentially localized in regions where $\xi$ takes large, and properly arranged, values. The picture we prove is thus closely connected with the phenomenon of Anderson localization at the spectral edge. Our proofs are largely independent of existing  methods for controlling Anderson localization and they permit a rather explicit description of the shape of the potential and the eigenfunctions.

(Joint work with M. Biskup)

 

16:45 Uhr: Margherita Disertori (Bonn): Random Schrödinger operators and history dependent stochastic processes

In the last years totally unexpected connections have been arising between lattice random Schrödinger operators and certain history dependent stochastic processes. I will give an overview and some recent results.

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Freitag, 09.02.2018

TU Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, Raum: tba:

Francesco Caravenna (University of Milano-Bicocca), Elisabetta Candellero (University of Warwick)

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Wegbeschreibungen

zur Anreise an die Uni Mainz finden Sie unter https://www.mathematik.uni-mainz.de/anfahrt/ , zur Anreise an die Uni Frankfurt unter https://www.uni-frankfurt.de/38074653/campus_bockenheim und https://www.uni-frankfurt.de/38093742/Campus_Bockenheim-pdf.pdf, zur Anreise an die TU Darmstadt unter http://www3.mathematik.tu-darmstadt.de/fb/mathe/wir-ueber-uns/adresse-und-lageplan/anreise.html

Termine in früheren Semestern finden Sie hier.

Last update: 12.12.2017, S. Grün, gruen@mathematik.uni-mainz.de