Let (Xnt ) be a Poisson sequence of independent Brownian motions in double-struck R signd, d ≧ 3; Let ℒ be a compact oriented submanifold of double-struck R signd, of dimension d - 2 and volume ℓ; let Φt, be the sum of the windings of (Xns, 0 ≦ s ≦ t) around ℒ; then Φt/t converges in law towards a Cauchy variable of parameter ℓ/2. A similar result is valid when the winding is replaced by the integral of a harmonic 1-form in double-struck R signd\ℒ.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty