151. Maximum of the Gaussian Interface Model in Random External Fields.
- Author
-
Sakagawa, Hironobu
- Subjects
- *
RANDOM variables , *RANDOM fields , *RANDOM matrices - Abstract
We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on R Λ N , Λ N = [ - N , N ] d ∩ Z d with Hamiltonian H N (ϕ) = 1 4 d ∑ x ∼ y (ϕ (x) - ϕ (y)) 2 - ∑ x ∈ Λ N η (x) ϕ (x) and 0-boundary conditions. { η (x) } x ∈ Z d is a family of i.i.d. symmetric random variables. We study how the typical maximal height of a random interface is modified by the addition of quenched bulk disorder. We show that the asymptotic behavior of the maximum changes depending on the tail behavior of the random variable η (x) when d ≥ 5 . In particular, we identify the leading order asymptotics of the maximum. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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