where ( n m ) ( n − − m ) ! counts the number of configurations in which those m particles around the tagged one have the optimal jumping order. Now, even when m~n/2, f ( n ) ∼ ∼ e − − n / 2 . Using in Eq. (21), f ( n ) ∼ ∼ e − − n / n 0 ( n 0 a small number larger than 1), we see,