IS11: Long Range Percolation Models

Organizer: Alexander Drewitz (Universität zu Köln)

Hausdorff dimension of the critical clusters for the metric graph Gaussian free field

Alexis Prévost

I will review recent results concerning the phase transition for a strongly correlated percolation model called the metric graph Gaussian free field. In particular, I will focus on the Hausdorff dimension of the critical connected components, as well as on the critical exponents which describe the volume of these components on graphs of intermediate dimension.