The Arboreal Gas

Date: 2022-08-11

Time: 14:00 - 15:00


Tyler Helmuth


In Bernoulli bond percolation each edge of a graph is declared open with probability p, and closed otherwise. Typically one asks questions about the geometry of the random subgraph of open edges. The arboreal gas is the probability measure obtained by conditioning on the event that the percolation subgraph is a forest, i.e., contains no cycles. Physically, this is a model for studying the gelation of branched polymers. What are the percolative properties of these random forests? Do they contain giant trees? I will discuss what is known and conjectured. Based on joint work with R. Bauerschmidt, N. Crawford, and A. Swan.