Geodesic
On the Distribution of Integer Random Variables Related by a Certain Linear Inequality.~III
Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 880-898.

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We consider tuples $\{N_{jk}\}$, $j=1,2,\dots$, $k=1,\dots,q_j$, of nonnegative integers such that $$ \sum_{j=1}^\infty\sum_{k=1}^{q_j} jN_{jk}\le M. $$ Assuming that $q_j\sim j^{d-1}$, $1$, we study how the probabilities of deviations of the sums $\sum_{j=j_1}^{j_2}\sum_{k=1}^{q_j} N_{jk}$ from the corresponding integrals of the Bose–Einstein distribution depend on the choice of the interval $[j_1,j_2]$.
Keywords: Bose–Einstein distribution, random variable, Euler–Maclaurin formula, strict convexity.
Mots-clés : Legendre transform, Gram matrix 
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V. P. Maslov; V. E. Nazaikinskii. On the Distribution of Integer Random Variables Related by a Certain Linear Inequality.~III. Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 880-898. http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a7/

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