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We prove Poincare inequalities w.r.t. the distributions of Brownian bridges on sets of loops with jumps of limited size over compact Riemannian manifolds. Moreover, we study the asymptotic behavior of the second Dirichlet eigenvalues as the time parameter T of the underlying Brownian bridge tends to 0. This behavior depends crucially on the geodesics contained in the set of loops considered. In particular,...
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