BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Phase transition of capacity for uniform \(G_{\delta}\) sets Quintino, Fernando

Description

We study the capacity of a uniform \(G_{\delta}\) set. Changing the speed at which the lengths of intervals generating it decrease, we observe a sharp phase transition from full to zero capacity. Such a $G_{\delta}$ set is also interesting because it can be considered as a model case for the set of exceptional energies in the parametric version of the Furstenberg theorem. In the talk, we will demonstrate the techniques used and as well as some interesting capacity-related examples.

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Attribution-NonCommercial-NoDerivatives 4.0 International