Geodesic
The maximum run length in generalized Bernoulli sequences
Diskretnaya Matematika, Tome 11 (1999) no. 1, pp. 29-52

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We study the distribution of the maximum length of runs of chosen types in some sequence of independent identically distributed random variables. Exact and asymptotic formulas for the distribution function of this maximum are obtained. The problem on the number of words with restrictions on the run lengths, which was considered earlier, is solved for the case of runs of several chosen types.The research was supported by the Russian Foundation for Basic Research, grant 96–01–01496. 
@article{DM_1999_11_1_a3,
     author = {L. Ja. Savel'ev},
     title = {The maximum run length in generalized {Bernoulli} sequences},
     journal = {Diskretnaya Matematika},
     pages = {29--52},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1999_11_1_a3/}
}
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L. Ja. Savel'ev. The maximum run length in generalized Bernoulli sequences. Diskretnaya Matematika, Tome 11 (1999) no. 1, pp. 29-52. http://geodesic.mathdoc.fr/item/DM_1999_11_1_a3/