@unpublished{KleinZitt2008, author = {Klein, Markus and Zitt, Pierre-Andr{\´e}}, title = {Resonances for a diffusion with small noise}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49448}, year = {2008}, abstract = {We study resonances for the generator of a diffusion with small noise in R(d) : L = -∈∆ + ∇F * ∇, 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.}, language = {en} }