%0 Journal Article
%T Resonances for a diffusion with small noise
%A Markus Klein
%A Pierre-Andr¨¦ Zitt
%J Mathematics
%D 2008
%I arXiv
%X We study resonances for the generator of a diffusion with small noise in $R^d$ :$ L_\epsilon = -\epsilon\Delta + \nabla F \cdot \nabla$, when the potential F grows slowly at infinity (typically as a square root of the norm). The case when F grows fast is well known, and under suitable conditions one can show that there exists a family of exponentially small eigenvalues, related to the wells of F . We show that, for an F with a slow growth, the spectrum is R+, but we can find a family of resonances whose real parts behave as the eigenvalues of the "quick growth" case, and whose imaginary parts are small.
%U http://arxiv.org/abs/0805.0106v1