 For large "s" the number of terms in the sum is large and according to general theorems of the ergodic theory the values of τs are distributed around formula_111 according to [[Gauss distribution|Gauss' law]] with the density
Calculation of the variance "D"τ is more complicated since not only the knowledge of formula_107 and formula_113 are needed but also of the correlations formula_114.The calculation can be simplified by rearranging the terms in the sum .By using the sum can be rewritten as

formula_115

The last two terms do not increase with increasing "s"; these terms can be omitted as the limiting laws for large "s" are dominating.