2019/06/06 by Christophe Garban, Garban, Christophe, Hugo Vanneuville +1 · 2 citations
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.1906.02666
openalex publication_date 2019/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that planar Bargmann-Fock percolation is noise sensitive under the Ornstein-Ulhenbeck process. The proof is based on the randomized algorithm approach introduced by Schramm and Steif and gives quantitative polynomial bounds on the noise sensitivity of crossing events for Bargmann-Fock. A rather counter-intuitive consequence is as follows. Let F be a Bargmann-Fock Gaussian field in ℝ3 and consider two horizontal planes P1,P2 at small distance ε from each other. Even though F is a.s. analytic, the above noise sensitivity statement implies that the full restriction of F to P1 (i.e. F| P1) gives almost no information on the percolation configuration induced by F|P2. As an application of this noise sensitivity analysis, we provide a Schramm-Steif based proof that the near-critical window of level line percolation around ℓc=0 is polynomially small. This new approach extends earlier sharp threshold results to a larger family of planar Gaussian fields.