Geodesic
The central limit theorem for the number of partial long duplications
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 4, pp. 880-884

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Let $X_1,X_2,\dots$ be a sequence of independent random variables, $X_i=1,2,\dots$. We prove the central limit theorem for the number of sets ($i_1,\dots,i_m$), $1\le i_1\dots$, such that the conditions $$ X_{i_1+k}=\dots=X_{i_m+k} $$ are satisfied for exactly $s-d$ values of $k\in\{0,\dots,s-1\}$. 
@article{TVP_1975_20_4_a16,
     author = {V. G. Mikhailov},
     title = {The central limit theorem for the number of partial long duplications},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {880--884},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_4_a16/}
}
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V. G. Mikhailov. The central limit theorem for the number of partial long duplications. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 4, pp. 880-884. http://geodesic.mathdoc.fr/item/TVP_1975_20_4_a16/