Exponential inequalities for the distribution of the number of cycles in the Erd\"os-R\'enyi random graph
Matematičeskie trudy, Tome 25 (2022) no. 1, pp. 63-73.

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

Exponential upper bounds are obtained for the tail probabilities of the centered and normalized number of cycles in the Erdös-Rényi graph.
@article{MT_2022_25_1_a2,
     author = {A. A. Bystrov and N. V. Volod'ko},
     title = {Exponential inequalities for the distribution of the number of cycles in the {Erd\"os-R\'enyi} random graph},
     journal = {Matemati\v{c}eskie trudy},
     pages = {63--73},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2022_25_1_a2/}
}
TY  - JOUR
AU  - A. A. Bystrov
AU  - N. V. Volod'ko
TI  - Exponential inequalities for the distribution of the number of cycles in the Erd\"os-R\'enyi random graph
JO  - Matematičeskie trudy
PY  - 2022
SP  - 63
EP  - 73
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2022_25_1_a2/
LA  - ru
ID  - MT_2022_25_1_a2
ER  - 
%0 Journal Article
%A A. A. Bystrov
%A N. V. Volod'ko
%T Exponential inequalities for the distribution of the number of cycles in the Erd\"os-R\'enyi random graph
%J Matematičeskie trudy
%D 2022
%P 63-73
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2022_25_1_a2/
%G ru
%F MT_2022_25_1_a2
A. A. Bystrov; N. V. Volod'ko. Exponential inequalities for the distribution of the number of cycles in the Erd\"os-R\'enyi random graph. Matematičeskie trudy, Tome 25 (2022) no. 1, pp. 63-73. http://geodesic.mathdoc.fr/item/MT_2022_25_1_a2/

[1] Bobkov S.G., Danshina M.A., and Ulyanov V.V., “Rate of convergence to the Poisson law of the number of cycles in the generalized random graphs. I”, OTHA 2020, Oper. Theory Harmon. Anal., Springer Proc. in Math. and Statist., 358, 2021, 109–132 | DOI | MR

[2] Borisov I. S., Bystrov A. A., “Eksponentsialnye neravenstva dlya raspredelenii kanonicheskikh protsessov chastichnykh kratnykh summ”, Teoriya veroyatn. i ee primen., 64:2 (2019), 209–227 | DOI | MR | Zbl

[3] Chatterjee S., “The missing log in large deviations for triangle counts”, Random Structures Algorithms, 40:4 (2011), 437–451 | DOI | MR

[4] Chatterjee S. and Varadhan S.R.S., “The large deviation principle for the Erdös-Rényi random graphs”, Eur. J. of Combin., 32:7 (2011), 1000–1017 | DOI | MR | Zbl

[5] DeMarco B. and Kahn J., “Upper tails for triangles”, Publ. Math. Inst. Hungar. Acad. Sci., 40:4 (2012), 452–459 | MR | Zbl

[6] Erdös P. and Rényi A., “On the evolution of random graphs”, Publ. Math. Inst. Hungar. Acad. Sci., 5 (1960), 38–82 | MR

[7] Höffding W., “Probability inequalities for sums of bounded random variables”, J. Amer. Statist. Assoc., 58 (1963), 13–30 | DOI | MR

[8] Janson S., Oleszkiewicz K., and Ruciński A., “Upper tails for subgraph counts in random graphs”, Israel J. Math., 142 (2004), 61–92 | DOI | MR | Zbl

[9] Kim J.H. and Vu V.H., “Divide and conquer martingales and the number of triangles in a random graph”, Random Structures Algorithms, 24:2 (2004), 166–174 | DOI | MR | Zbl

[10] Liu Q. and Dong Z., “Limit laws for the number of triangles in the generalized random graphs with random node weights”, Statist. Probab. Lett., 161:1 (2020), 1–6 | DOI | MR

[11] A. V., Mogulskii A. A., “Eksponentsialnye neravenstva Chebysheva dlya sluchainykh grafonov i ikh primenenie”, Sib. matem. zhurn., 6:4 (2020), 880–900

[12] Ruciński A., When are small subgraphs of a random graph normally distributed?, Probab. Theory Related Fields, 78:1 (1988), 1–10 | DOI | MR | Zbl