Wendelin Werner
Published 2020-02-26Version 1
We discuss random geometric structures obtained by percolation of Brownian loops, in relation to the Gaussian Free Field, and how their existence and properties depend on the dimension of the ambient space. We formulate a number of conjectures for the cases d=3,4,5 and prove some results when d > 6.
On decoupling inequalities and percolation of excursion sets of the Gaussian free field
Local metrics of the Gaussian free field
Coupling the Gaussian free fields with free and with zero boundary conditions via common level lines
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