2020/09/30 by Alain-Sol Sznitman, Alain‐Sol Sznitman
Mathematics · Physics and Astronomy · #Boundary (topology) #Combinatorics #Exponential decay #Exponential function #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Percolation (cognitive psychology) #Physics #Quantum mechanics #Stochastic processes and statistical mechanics #Upper and lower bounds #math-ph #math.MP #math.PR #msc:35A15 #msc:60F10 #msc:60K35 #msc:82B43
paper · pdf · doi:10.2140/pmp.2021.2.563
published as Prob. Math. Phys. 2 (2021) 563-611 · 46 pages, 3 figures, to appear in Probability and Mathematical Physics
arxiv created 2021/06/08 · openalex publication_date 2021/10/15 · arxiv updated 2021/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider random interlacements on ℤd, d ≥ 3, when their vacant set is in a strongly percolative regime. Given a large box centered at the origin, we establish an asymptotic upper bound on the exponential rate of decay of the probability that the box contains an excessive fraction ν of points that are disconnected by random interlacements from the boundary of a concentric box of double size. As an application we show that when ν is not too large, this asymptotic upper bound matches the asymptotic lower bound derived in a previous work of the author, and the exponential rate of decay is governed by a certain variational problem in the continuum which involves the percolation function of the vacant set of random interlacements.