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
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
so
 |  |  |
(4)
|
 |  |  |
(5)
|
which is called the mean run count per site or mean run density in percolation theory.
