The critical threshold for Bargmann-Fock percolation

Vortrag von Dr. Hugo Vanneuville

Datum: 10.05.17  Zeit: 17.15 - 19.00  Raum: Y27H12

Let f be the planar Bargmann-Fock field, which is the analytic Gaussian field with covariance kernel exp(-1/2|x-y|²). We compute the critical point for the percolation model induced by the level sets of f. More precisely, we prove that there exists a.s. an unbounded component in {f>p} if and only if p<0. One important aspect of our work is a new way of controlling generalized influences. This is joint work with Alejandro Rivera.