Université Paris-Est Université Paris-Est - Marne-la-Vallée Université Paris-Est - Créteil Val-de-Marne Centre National de la Recherche Scientifique

Potentials, energies and Hausdorff dimension

Site: 
Date: 
11/01/2018 - 13:45 - 14:45
Salle: 
P1 P15
Orateur: 
PERSSON Tomas
Localisation: 
Université de Lund
Localisation: 
Suède
Résumé: 

There is a classical connection between Riesz-potentials, Riesz-energies and Hausdorff dimension. Otto Frostman (Lund) proved in his thesis that if $E$ is a set and $\mu$ is a measure with support in $E$, then the Hausdorff dimension of $E$ is at least $s$ if the $s$-dimensional Riesz-energy of $\mu$ is finite. I will first recall Frostman’s result and some of its applications. I will then mention some new methods where Hausdorff dimension is calculated using potentials and energies with inhomogeneous kernels. Some applications are in stochastic geometry and dynamical systems.