A switching property for Brownian loop-soups
I will describe a model of random non-interacting Brownian loops, its motivations and relevance to physics, and then discuss a recent result about percolation of such loops and some of its consequences. This "switching property" is that conditioning two given points to be connected by a chain of loops is (in terms of the picture of clusters of loops) equivalent to adding a random odd number of excursions between these two points to an otherwise unconditioned configurations of Brownian loops.