Geodesic
Asymptotics of the Shannon entropy for sums of independent random variables
Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 4, pp. 1019-1028.

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With the help of the local limit theorem we investigate the asymptotics of the Shannon entropy for sums of independent identically distributed random variables. 
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     author = {A. G. D'yachkov},
     title = {Asymptotics of the {Shannon} entropy for sums of independent random variables},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1996_2_4_a4/}
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A. G. D'yachkov. Asymptotics of the Shannon entropy for sums of independent random variables. Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 4, pp. 1019-1028. http://geodesic.mathdoc.fr/item/FPM_1996_2_4_a4/