Estimates of the mean size of the subset image under composition of random mappings
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Andrey M. Zubkov
und
Aleksandr A. Serov
Abstract
Let XN be a set of N elements and F1, F2,… be a sequence of random independent equiprobable mappings XN → N. For a subset S0 ⊂ XN, |S0|=m, we consider a sequence of its images St=Ft(…F2(F1(S0))…), t=1,2… An approach to the exact recurrent computation of distribution of |St| is described. Two-sided inequalities forM{|St|||S0|=m} such that the difference between the upper and lower bounds is o(m)for m, t, N → ∞, mt=o(N) are derived. The results are of interest for the analysis of time-memory tradeoff algorithms.
Note: Originally published in Diskretnaya Matematika (2018) 30, N∘2, 27–36 (in Russian).
Communicated by Anatolij Dvurečenskij
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A subcritical decomposable branching process in a mixed environment
- Limit theorems for bounded branching processes
- On coincidences of tuples in a q-ary tree with random labels of vertices
- A generalization of Shannon function
- Reduced critical Bellman–Harris branching processes for small populations
- Estimates of the mean size of the subset image under composition of random mappings
- Necessary conditions for power commuting in finite-dimensional algebras over a field
Artikel in diesem Heft
- Frontmatter
- A subcritical decomposable branching process in a mixed environment
- Limit theorems for bounded branching processes
- On coincidences of tuples in a q-ary tree with random labels of vertices
- A generalization of Shannon function
- Reduced critical Bellman–Harris branching processes for small populations
- Estimates of the mean size of the subset image under composition of random mappings
- Necessary conditions for power commuting in finite-dimensional algebras over a field
