Potentials, energies and Hausdorff dimension

Orateur: PERSSON Tomas
Localisation: Université de Lund, Suède
Type: Séminaire cristolien d'analyse multifractale
Site: UPEC
Salle: P1 P15
Date de début: 11/01/2018 - 13:45
Date de fin: 11/01/2018 - 14:45

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.