Switching identities for loop-soups and consequences
Appears in collection : Perfectly matched perspectives on statistical mechanics, combinatorics and geometry / Perspectives couplées sur la mécanique statistique, la combinatoire et la géométrie
I will describe new and possibly surprising identities in law for loop-soups and Gaussian Free Fields on cable graphs, that allow to describe in simple terms the law of configurations when conditioned on connections to exist. I will discuss some consequences, including in directions inspired by Rick Kenyon's ideas.
