### Percolation of worms

Probability Seminar

15th October 2021, 3:30 pm – 4:30 pm

Fry Building, 2.04 (also on Zoom)

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 and compare it to related results about similar

models from the literature. We also 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.

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