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math.PR2026
Brownian Loops, Singular Homology, and Asymptotic Cycles
Alberto Verjovsky, Ricardo F. Vila-Freyer
Let be a closed connected Riemannian manifold. A continuous semimartingale segment can be closed by a Borel family of paths of uniformly bounded length, producing a singular ho…
math.PR2023
Asymptotic Homology of Brownian motion on a Riemannian manifold
Alberto Verjovsky, Ricardo F. Vila-Freyer
We prove, using the celebrated result by Spitzer about winding of planar Brownian motion, and the existence of harmonic morphisms representing cohomology clas…