14:15
Brownian motion in tubular neighborhoods around closed Riemannian submanifolds
Abstract
We consider Brownian motion on a manifold conditioned not to leave
the tubular neighborhood of a closed riemannian submanifold up
to some fixed finite time. For small tube radii, it behaves like the
intrinsic Brownian motion on the submanifold coupled to some
effective potential that depends on geometrical properties of
the submanifold and of the embedding. This characterization
can be applied to compute the effect of constraining the motion of a
quantum particle on the ambient manifold to the submanifold.