Probability that given vertices belong to the same connected component of random equiprobable mapping
-
Andrey M. Zubkov
und
Petr V. Khalipov
Abstract
The random equiprobable mappings of finite set S into itself are considered. The probability that k fixed elements of S belong to the same connected component is studied. The limit of this probability as |S| → ∞ is found.
Originally published in Diskretnaya Matematika (2022) 34, №4, 28–35 (in Russian).
References
[1] Harris B., “Probability distributions related to random mappings”, Ann. Math. Statist., 31:4 (1960), 1045–1062.10.1214/aoms/1177705677Suche in Google Scholar
[2] Kolchin V. F., Random Mappings, Optimization Software Inc. Publications Division, New York, 1986, 207 pp.Suche in Google Scholar
[3] Zubkov A. M., Khalipov P. V., “On the probability of falling several points into one random mapping component”, Obozr. prikl. i promyshl. matem., 16:3 (2009) (in Russian).Suche in Google Scholar
[4] Pittel B., “On distibutions related to transitive closures of random finite mappings”, Ann. Probab., 11:2 (1983), 428–441.10.1214/aop/1176993608Suche in Google Scholar
[5] Mironkin V. O., “The probability of two random points collision for the degree of random mapping”, Obozr. prikl. i promyshl. matem., 22:4 (2015), 403–409 (in Russian).Suche in Google Scholar
[6] Mironkin V. O., “Collisions and the incidence of vertices to components in the graph of k-fold iteration of a uniform random mapping”, Discrete Math. Appl., 31:4 (2021), 259–269.10.1515/dma-2021-0023Suche in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On large deviations of the moment of attaining far level by the random walk in a random environment
- Asymptotic local lower deviations of strictly supercritical branching process in a random environment with geometric distributions of descendants
- Cloning operations and graph diameter
- Relations between energy complexity measures of Boolean networks and positive sensitivity of Boolean functions
- On the maximal size of tree in a random forest
- Deciding multiaffinity of polynomials over a finite field
- Probability that given vertices belong to the same connected component of random equiprobable mapping
Artikel in diesem Heft
- Frontmatter
- On large deviations of the moment of attaining far level by the random walk in a random environment
- Asymptotic local lower deviations of strictly supercritical branching process in a random environment with geometric distributions of descendants
- Cloning operations and graph diameter
- Relations between energy complexity measures of Boolean networks and positive sensitivity of Boolean functions
- On the maximal size of tree in a random forest
- Deciding multiaffinity of polynomials over a finite field
- Probability that given vertices belong to the same connected component of random equiprobable mapping
