Balazs Rath: Percolation of worms

We introduce a new correlated percolation model on the \(d\)-dimensional lattice \(Z^d\) called the random length worms model. Our main contribution is a sufficient condition on the length distribution of worms which guarantees that there is no percolation phase transition if \(d >= 5\).

We argue that this sufficient condition is quite close to being sharp. If time permits, we compare it to related results about similar models from the literature. Alternatively, we can discuss the methods of our proof: dynamic renormalization, bounds on the capacity of random walk trajectories and a recursive construction which involves a rapidly growing sequence of scales. 

Joint work with Sándor Rokob.