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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{MZM_2008_83_6_a7,
     author = {V. P. Maslov and V. E. Nazaikinskii},
     title = {On the {Distribution} of {Integer} {Random} {Variables} {Related} by a {Certain} {Linear} {Inequality.~III}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {880--898},
     publisher = {mathdoc},
     volume = {83},
     number = {6},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a7/}
}
TY  - JOUR
AU  - V. P. Maslov
AU  - V. E. Nazaikinskii
TI  - On the Distribution of Integer Random Variables Related by a Certain Linear Inequality.~III
JO  - Matematičeskie zametki
PY  - 2008
SP  - 880
EP  - 898
VL  - 83
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a7/
LA  - ru
ID  - MZM_2008_83_6_a7
ER  - 
%0 Journal Article
%A V. P. Maslov
%A V. E. Nazaikinskii
%T On the Distribution of Integer Random Variables Related by a Certain Linear Inequality.~III
%J Matematičeskie zametki
%D 2008
%P 880-898
%V 83
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a7/
%G ru
%F MZM_2008_83_6_a7
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/