Semi-classical asymptotics for scattering length of symmetric stable processes

Daehong Kim and Masakuni Matsuura

Statistics & Probability Letters, 2020, vol. 167, issue C

Abstract: In this paper we study the problem of semi-classical asymptotics for the scattering length of non-negative potentials with infinite range. It was proved analytically by Tamura (1993) that the scattering length Γ(V) of a non-negative V induced by 3-dimensional Brownian motion obeys Γ(ε−2V)∼ε−2∕(ρ−2) in the semi-classical limit ε→0, if V(x) behaves like |x|−ρ,ρ>3 at infinity. We will extend this result probabilistically for the scattering length of non-negative potentials including a jumping function under the framework of symmetric stable processes.

Keywords: Additive functionals; Scattering lengths; Semi-classical asymptotics; Symmetric stable process (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108921

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