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 
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/
@article{ZNSL_2012_408_a3,
     author = {S. G. Bobkov and G. P. Chistyakov},
     title = {Bounds on the maximum of the density for sums of independent random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {62--73},
     year = {2012},
     volume = {408},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_408_a3/}
}
TY  - JOUR
AU  - S. G. Bobkov
AU  - G. P. Chistyakov
TI  - Bounds on the maximum of the density for sums of independent random variables
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2012
SP  - 62
EP  - 73
VL  - 408
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2012_408_a3/
LA  - ru
ID  - ZNSL_2012_408_a3
ER  - 
%0 Journal Article
%A S. G. Bobkov
%A G. P. Chistyakov
%T Bounds on the maximum of the density for sums of independent random variables
%J Zapiski Nauchnykh Seminarov POMI
%D 2012
%P 62-73
%V 408
%U http://geodesic.mathdoc.fr/item/ZNSL_2012_408_a3/
%G ru
%F ZNSL_2012_408_a3

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] A. Dembo, T. M. Cover, J. A. Thomas, “Information-theoretic inequalities”, IEEE Trans. Inform. Theory, 37:6 (1991), 1501–1518 | DOI | MR | Zbl

[2] O. Johnson, Information Theory and the Central Limit Theorem, Imperial College Press, London, 2004 | MR | Zbl

[3] S. G. Bobkov, M. Madiman, “Reverse Brunn–Minkowski and reverse entropy power inequalities for convex measures”, J. Funct. Anal., 262:7 (2012), 3309–3339 | DOI | MR | Zbl

[4] A. J. Stam, “Some inequalities satisfied by the quantities of information of Fisher and Shannon”, Information Control, 2 (1959), 101–112 | DOI | MR | Zbl

[5] V. V. Petrov, Summy nezavisimykh sluchainykh velichin, Fizmatlit, M., 1972 | MR

[6] A. N. Shiryaev, Veroyatnost, Nauka, M., 1980 | MR | Zbl

[7] S. G. Bobkov, G. P. Chistyakov, F. Götze, “Bounds for characteristic functions in terms of quantiles and entropy”, Electron. Commun. Probab., 17 (2012), Article 21, 9 pp. | DOI | MR | Zbl

[8] E. H. Lieb, “Proof of an entropy conjecture of Wehrl”, Comm. Math. Phys., 62:1 (1978), 35–41 | DOI | MR | Zbl

[9] W. Beckner, “Inequalities in Fourier analysis”, Ann. Math., 2:1 (1975), 159–182 | DOI | MR | Zbl

[10] H. J. Brascamp, E. H. Lieb, “Best constants in Young's inequality, its converse, and its generalization to more than three functions”, Advances Math., 20:2 (1976), 151–173 | DOI | MR | Zbl

[11] F. Barthe, “Optimal Young's inequality and its converse: a simple proof”, Geom. Funct. Anal., 8:2 (1998), 234–242 | DOI | MR | Zbl

[12] S. G. Bobkov, C. Houdre, P. Tetali, “The subgaussian constant and concentration inequalities”, Israel J. Math., 156 (2006), 255–283 | DOI | MR | Zbl

[13] B. A. Rogozin, “Otsenka maksimuma svertki ogranichennykh plotnostei”, Teoriya veroyatn. i ee primen., 32:1 (1987), 53–61 | MR | Zbl

[14] Yu. V. Prokhorov, “Ekstremalnye zadachi v predelnykh teoremakh”, Trudy VI Vsesoyuznogo soveschaniya po teorii veroyatnostei i matematicheskoi statistike, Gos. izd-vo polit. i nauchn. liter. Lit.SSR, Vilnyus, 1962, 77–84

[15] K. Ball, “Cube slicing in $\mathbf R^n$”, Proc. Amer. Math. Soc., 97:3 (1986), 465–473 | MR | Zbl

[16] K. Ball, “Some remarks on the geometry of convex sets”, Lect. Notes Math., 1317, 1988, 224–231 | DOI | MR | Zbl

[17] L. P. Postnikova, A. A. Yudin, “Usilennaya forma dlya funktsii kontsentratsii”, Teoriya veroyatn. i ee primen., 23:2 (1978), 376–379 | MR | Zbl

[18] A. L. Miroshnikov, B. A. Rogozin, “Neravenstva dlya funktsii kontsentratsii”, Teoriya veroyatn. i ee primen., 25:1 (1980), 178–183 | MR | Zbl