We seek a global minimum of $U:[0,1]^n \to R$. The solution to $({d / {dt}})x_t = - \nabla U(x_t )$ will find local minima. The solution to $dx_t = - \nabla U(x_t )dt + \sqrt {2T} dw_t $, where w is standard (n-dimensional) Brownian motion and the boundaries are reflecting, will concentrate near the...
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