The present paper is concerned with some self-interacting diffusions (xt,t = 0) living on Rd. These diffusions are solutions to\nstochastic differential equations: dxt = dbt\n- g(t)?V(xt - �µ �¯??)????, where ???? is the empirical mean of the process ??, ?? is an\nasymptotically strictly convex potential, and g is a given positive function. We study the asymptotic behaviour of x for three\ndifferent families of functions g. If g (t) = k log t with k small enough, then the process x converges in distribution towards the\nglobal minima of V, whereas if tg(t) ? c ?]0, ] or if g(t) ? g(8) ? [0, [, then x converges in distribution if and only\nif?xe-2V(x)dx = 0.
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