Affiliation:
1. Département de Mathématiques , Université de Reims , Moulin de la Housse, B.P.1039, 51687 Reims Cedex , France
Abstract
Abstract
We study random displacements models with a long-range particle-media interaction potential
𝔲
(
r
,
θ
)
=
𝔣
(
θ
)
r
-
A
{\mathfrak{u}(r,\theta)=\mathfrak{f}(\theta)r^{-A}}
in polar coordinates, with a smooth function
𝔣
{\mathfrak{f}}
which can be sign-indefinite.
Spectral and dynamical localization, with an asymptotically exponential decay of eigenfunction correlators,
is proved under the optimal condition
A
>
d
{A>d}
.
Subject
Statistics and Probability,Analysis