Small Mass Limit of a Langevin Equation on a Manifold

Abstract

We study damped geodesic motion of a particle of mass $m$ on a Riemannian manifold, in the presence of an external force and noise. Lifting the resulting stochastic differential equation to the orthogonal frame bundle, we prove that, as $m\to 0$, its solutions converge to solutions of a limiting equation which includes a {\it noise-induced drift} term. A very special case of the main result presents Brownian motion on the manifold as a limit of inertial systems.

48 pages

References in corpus (2)

• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• The Small-Mass Limit for Langevin Dynamics with Unbounded Coefficients and positive friction

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