Geodesic
Limit theorems for the number of dense series in a~random sequence
Diskretnaya Matematika, Tome 21 (2009) no. 1, pp. 105-116.

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We investigate the joint distribution of the number of dense series in a random sequence over a finite alphabet. With the use of the Chen–Stein method, we find estimates of the distance in variation between the distribution of the vector of the numbers of dense series of ones of given lengths and the accompanying multidimensional Poisson distribution. These estimates give a possibility to prove limit theorems of Poisson type for the numbers of dense series of ones of given lengths and of lengths no less than a given length, for the number of intervals densely filled by ones, a limit theorem for the maximal length of dense series of ones, and a limit theorem for the number of dense series of ones of a given weight. 
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N. M. Mezhennaya. Limit theorems for the number of dense series in a~random sequence. Diskretnaya Matematika, Tome 21 (2009) no. 1, pp. 105-116. http://geodesic.mathdoc.fr/item/DM_2009_21_1_a5/

[1] Barbour A. D., Holst L., Janson S., Poisson approximation, Oxford Univ. Press, Oxford, 1992 | MR | Zbl

[2] Golić J. D., “Constrained embedding probability for two binary strings”, SIAM J. Discrete Math., 9:3 (1996), 360–364 | DOI | MR | Zbl

[3] Mikhailov V. G., Mezhennaya N. M., “Otsenki dlya veroyatnosti plotnogo vlozheniya odnoi diskretnoi posledovatelnosti v druguyu”, Diskretnaya matematika, 17:3 (2005), 19–27 | MR | Zbl

[4] Mezhennaya N. M., “Predelnye teoremy dlya chisla plotnykh serii v sluchainoi posledovatelnosti”, Nauchno-tekhnicheskaya konferentsiya studentov, aspirantov i molodykh spetsialistov MIEM, MIEM, Moskva, 2008, 11–13

[5] Mezhennaya N. M., “O skorosti skhodimosti raspredeleniya chisla serii razlichnoi dliny v sluchainoi posledovatelnosti s “razladkami” k raspredeleniyu Puassona”, Obozrenie prikladnoi i promyshlennoi matematiki, 14:2 (2007), 248–249