Geodesic
On the limit behaviour of the maximal probability in infinite dimensional case
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 4, pp. 753-754

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It is shown that in infinite dimensional case the maximal probabilities of distributions which are convolutions of a lattice distribution descend to 0 quicker than any negative power of $n$. Moreover the limits for the speed of their convergence are indicated. 
@article{TVP_1965_10_4_a15,
     author = {V. V. Sazonov},
     title = {On the limit behaviour of the maximal probability in infinite dimensional case},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {753--754},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {1965},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_4_a15/}
}
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V. V. Sazonov. On the limit behaviour of the maximal probability in infinite dimensional case. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 4, pp. 753-754. http://geodesic.mathdoc.fr/item/TVP_1965_10_4_a15/