*N.B. A detailed on-line essay by S. Finch
was the starting point for this entry.*

Let be a -Vector whose entries are each 1 (with probability ) or 0 (with probability ).
An -run is an isolated group of consecutive 1s. Ignoring the boundaries, the total number of runs satisfies

so

which is called the Mean Run Count Per Site or Mean Run Density in Percolation Theory.

**References**

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/rndprc/rndprc.html

© 1996-9

1999-05-26