Let v be a n-vector whose entries are each 1 (with probability p) or 0 (with probability q = 1 - p). An s-run is an isolated group of s consecutive 1s. Ignoring the boundaries, the total number of runs R_n satisfies K_n | = | (〈R_n 〉)/n | = | (1 - p)^2 sum_(s = 1)^n p^s | = | p(1 - p)(1 - p^n), so K(p) | congruent | lim_(n->∞) K_n | = | p(1 - p), which is called the mean run count per site or mean run density in percolation theory.
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