Estimates of the mean size of the subset image under composition of random mappings
Copyright policy )Estimates of the mean size of the subset image under composition of random mappings
Abstract Let X N be a set of N elements and F 1 , F 2 ,… be a sequence of random independent equiprobable mappings X N → N . For a subset S 0 ⊂ X N , | S 0 |= m , we consider a sequence of its images S t = F t (… F 2 ( F 1 ( S 0 ))…), t =1,2… An approach to the exact recurrent computation of distribution of | S t | is described. Two-sided inequalities for M {| S t ||| S 0 |= 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.
compositions of random mappings, time-memory tradeoff method, Central limit and other weak theorems, Probability distributions: general theory
compositions of random mappings, time-memory tradeoff method, Central limit and other weak theorems, Probability distributions: general theory
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