Escape times of j random walkers from a fractal labyrinth

The problem of the statistical description of the first passage time t(j,N) to a given distance r of the first j of a set of N noninteracting diffusing particles, all starting from the same origin on fractal substrates, is addressed. Asymptotic expressions (the main and two corrective terms) for large N of the (arbitrary) moments of t(j,N) are given. It is shown that, to first order and for 1 less than or equal to j << N, the mth moment of t(j,N) goes as (ln N)(m(1-dw)), and its variance as (ln N)(-2dw), d(w) being the anomalous diffusion exponent of the fractal medium. [S0031-9007(97)04503-1].