Leírás
Előadó: Daniel Valesin
Cím: Monotonicity for multi-range percolation on oriented trees
Absztrakt: Percolation theory contains a variety of monotonicity-related conjectures which are easy and natural to state but challenging to prove. In this talk, we will survey a few of these problems. We will then specialize to the setting of Bernoulli percolation on multi-range oriented trees. The trees we consider are oriented regular trees where besides the usual short bonds, all bonds of a certain length are added. Independently, short bonds are open with probability p and long bonds are open with probability q. We study properties of the critical curve which delimits the set of pairs (p,q) for which there is percolation. We also show that this curve decreases with respect to the length of the long bonds. Joint work with Bernardo N. B. de Lima and Leonardo T. Rolla.