Geodesic
Variance of the additive weight deficit of equiprobable involution on the residue group
Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 3, pp. 101-116 
V. N. Sachkov; I. A. Kruglov. Variance of the additive weight deficit of equiprobable involution on the residue group. Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 3, pp. 101-116. http://geodesic.mathdoc.fr/item/MVK_2019_10_3_a6/
@article{MVK_2019_10_3_a6,
     author = {V. N. Sachkov and I. A. Kruglov},
     title = {Variance of the additive weight deficit of equiprobable involution on the residue group},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {101--116},
     year = {2019},
     volume = {10},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2019_10_3_a6/}
}
TY  - JOUR
AU  - V. N. Sachkov
AU  - I. A. Kruglov
TI  - Variance of the additive weight deficit of equiprobable involution on the residue group
JO  - Matematičeskie voprosy kriptografii
PY  - 2019
SP  - 101
EP  - 116
VL  - 10
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MVK_2019_10_3_a6/
LA  - ru
ID  - MVK_2019_10_3_a6
ER  - 
%0 Journal Article
%A V. N. Sachkov
%A I. A. Kruglov
%T Variance of the additive weight deficit of equiprobable involution on the residue group
%J Matematičeskie voprosy kriptografii
%D 2019
%P 101-116
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/MVK_2019_10_3_a6/
%G ru
%F MVK_2019_10_3_a6

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

We find exact and asymptotic formulas for the variance of the random variable $\zeta_n$ which is equal to the weight deficit of random involution defined on the additive group of residues modulo natural number $n$. The asymptotic formula for $n\to\infty$ has the following form: $$ \mathbf{D}{{\zeta}_{n}}=n\left(e^{-\frac{1}{2}}-\frac{3}{2}{{e}^{-1}} \right)\left(1+O\left(\frac{1}{n^{\frac{1}{3}}} \right) \right). $$

[1] Sachkov V. N., “Kombinatornye svoistva differentsialno 2-ravnomernykh podstanovok”, Matematicheskie voprosy kriptografii, 6:1 (2015), 159–180 | DOI | MR

[2] Sachkov V. N., Kruglov I. A., “Vesovye defitsity involyutsii i podstanovok”, Matematicheskie voprosy kriptografii, 7:4 (2016), 95–116 | DOI | MR

[3] Sachkov V. N., “Involyutsii s dannym vesovym defitsitom, sootvetstvuyuschie tablitse Keli konechnoi abelevoi gruppy”, Matematicheskie voprosy kriptografii, 8:4 (2017), 117–134 | DOI | MR

[4] Sachkov V. N., Kruglov I. A., “Momenty vesovogo defitsita sluchainoi ravnoveroyatnoi involyutsii, deistvuyuschei na konechnom vektornom prostranstve nad polem iz dvukh elementov”, Matematicheskie voprosy kriptografii, 9:4 (2018), 101–124 | DOI | MR

[5] Sachkov V. N., Kurs kombinatornogo analiza, NITs «Regulyarnaya i khaoticheskaya dinamika», Moskva–Izhevsk, 2013, 336 pp.