satisfies a nonlinear evolution starting with the probability distribution η η 0 ( d x 0 ) = p ( x 0 ) d x 0 . One of the simplest ways to approximate these probability measures is to start with N independent random variables ( ξ ξ 0 i ) 1 ⩽ ⩽ i ⩽ ⩽ N with common probability distribution η η 0 ( d x 0 ) = p ( x 0 ) d x 0 . Suppose we have defined a sequence of N random variables ( ξ ξ n i ) 1 ⩽ ⩽ i ⩽ ⩽ N such that