PrerequisiteConditional expectation and Discrete MartingalesIntroductionGaussian vectors.Brownian motion: Construction, continuity, nondifferentiability.Strong Markov propertyMultidimensional BM: harmonic functions, recurrence and transienceSkorokhod embedding and the Law of the iterated logarithmStochastic integral and Ito formula with respect to BMConformal invariance of Brownian motion paths...
AbstractKinetic Brownian motion is a stochastic process that interpolates between the geodesic flow and Laplacian. It is also an analogue of Bismut’s hypoelliptic Laplacian. We prove the strong convergence of the spectrum of kinetic Brownian motion to the spectrum of base Laplacian for all compact Riemannian manifolds. This generalizes recent work of Kolb--Weich--Wolf on constant curvature sur...