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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
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