Geodesic
Bounds on the maximum of the density for sums of independent random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 18, Tome 408 (2012), pp. 62-73

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Sublinear bounds on the maximum of the density for sums of independent random variables are given in terms of the maxima of the densities of the summands. 
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     author = {S. G. Bobkov and G. P. Chistyakov},
     title = {Bounds on the maximum of the density for sums of independent random variables},
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S. G. Bobkov; G. P. Chistyakov. Bounds on the maximum of the density for sums of independent random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 18, Tome 408 (2012), pp. 62-73. http://geodesic.mathdoc.fr/item/ZNSL_2012_408_a3/