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Let M be a compact Riemannian manifold. A self-interacting diffusion on M is a stochastic process solution to dX t = dW t (X t) − 1 t t 0 ∇V Xs (X t)ds dt where {W t } is a Brownian vector field on M and V x (y) = V (x, y) a smooth function. Let µ t = 1 t t 0 δ Xs ds denote the normalized occupation measure of X t. We prove that, when V is symmetric, µ t(More)
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