Geodesic
Limit distributions of the number of absent chains of identical outcomes
Diskretnaya Matematika, Tome 20 (2008) no. 3, pp. 40-46.

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We prove the asymptotic normality of the number of absent $s$-chains of identical outcomes in the equiprobable polynomial scheme under the condition that the number of trials $n$ and the number of outcomes $N$ tend to infinity in such a way that $\alpha_N=n/N^s\to\alpha$, $0\le\alpha\infty$, $N\alpha_N^2\to\infty$. 
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M. I. Tikhomirova. Limit distributions of the number of absent chains of identical outcomes. Diskretnaya Matematika, Tome 20 (2008) no. 3, pp. 40-46. http://geodesic.mathdoc.fr/item/DM_2008_20_3_a3/

[1] Basharin G. P., “Ob ispolzovanii kriteriya soglasiya $\chi^2$ v kachestve kriteriya nezavisimykh ispytanii”, Teoriya veroyatnostei i ee primeneniya, 2:1 (1957), 141–142 | Zbl

[2] Tikhomirova M. I., “Predelnye raspredeleniya statistik $\chi^2$ dlya chastot tsepochek odinakovykh iskhodov polinomialnoi skhemy”, Trudy po diskretnoi matematike, 7, 2003, 191–200

[3] Tikhomirova M. I., Chistyakov V. P., “Predelnye raspredeleniya nekotorykh statistik, svyazannykh s rekurrentnymi sobytiyami”, Trudy po diskretnoi matematike, 7, 2003, 201–212 | MR

[4] Tikhomirova M. I., Predelnye teoremy dlya chisla nepoyavivshikhsya $s$-tsepochek, Dis. $\dots$ kand. fiz.-matem. nauk, MIEM, Moskva, 1998

[5] Tikhomirova M. I., Chistyakov V. P., “Ob asimptotike momentov chisla nepoyavivshikhsya $s$-tsepochek”, Diskretnaya matematika, 9:1 (1997), 12–29 | MR | Zbl

[6] Kolchin V. F., Sevastyanov B. A., Chistyakov V. P., Sluchainye razmescheniya, Nauka, Moskva, 1976 | MR | Zbl

[7] Bernshtein S. N., Sobranie sochinenii, T. 6, Nauka, Moskva, 1964

[8] Janson S., “Normal convergence by higher semiinvariants with application to sums of dependent random variables and random graphs”, Ann. Probab., 16:1 (1988), 305–312 | DOI | MR | Zbl

[9] Mikhailov V. G., “Asimptoticheskaya normalnost razdelimykh statistik ot chastot $m$-tsepochek”, Diskretnaya matematika, 1:4 (1989), 92–103 | MR | Zbl