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Uniform convergence of random functions on amenable groups
Summary
This project aims to show and quantify the uniform almost-sure convergence of function-valued random fields over the power set of a
finitely generated amenable group along a Følner sequence.
Asymptotics for these convergences have already been established in many cases, however a fully quantified bound is still missing.
Important parts of this research are the theory of amenable groups, specifically \(\epsilon\)-quasitilings, multivariate Glivenko-Cantelli theorems and the theory of empirical processes.
An example of an applicatication is the convergence of eigenvalue-counting functions for Anderson operators on finite lattices to the integrated density of states of the operator on the whole lattice.
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Literature
- Uniform Existence of the IDS on Lattices and Groups. Christoph Schumacher, Fabian Schwarzenberger, Ivan Veselić (2020). In: Analysis and Geometry on Graphs and Manifolds, pp. 445–478. Cambridge University Press. [DOI] [arXiv]
- Glivenko-Cantelli theory, Ornstein-Weiss quasi-tilings, and uniform ergodic theorems for distribution-valued fields over amenable groups. Christoph Schumacher, Fabian Schwarzenberger, Ivan Veselić (2018). In: The Annals of Applied Probability, Volume 28, Issue 4, pp. 2417–2450. [DOI] [arXiv]
- A Glivenko-Cantelli theorem for almost additive functions on lattices. Christoph Schumacher, Fabian Schwarzenberger, Ivan Veselić (2017). In: Stochastic Processes and their Applications, Volume 127, Issue 1, pp. 179–208. [DOI] [arXiv]
Kontakt
Adresse
TU Dortmund
Fakultät für Mathematik
Lehrstuhl IX
Vogelpothsweg 87
44227 Dortmund
Sie finden uns auf dem sechsten Stock des Mathetowers.
Sekretariat
Janine Textor (Raum M 620)
Tel.: (0231) 755-3063
Fax: (0231) 755-5219
Mail: janine.textor@tu-dortmund.de
Bürozeiten:
Di. und Do. von 8 bis 12 Uhr
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