The Arboreal Gas

27.03.2023 16:15 – 18:15

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. Mathematically it is the q->0 limit of the random cluster model. What are the percolative properties of these random forests? Do they contain giant trees? I will discuss what is known, what is conjectured, and how a connection with spin systems allows for analysis and intuition.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Maths-Physique"

entrée libre