naa a22 4500 510812090 CHVBK 20180411083447.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1134/S0081543813060217 doi (NATIONALLICENCE)springer-10.1134/S0081543813060217 Yakymiv A. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russia aut Random A -permutations and Brownian motion [Elektronische Daten] [A. Yakymiv] We consider a random permutation τ n uniformly distributed over the set of all degree n permutations whose cycle lengths belong to a fixed set A (the so-called A-permutations). Let X n (t) be the number of cycles of the random permutation τ n whose lengths are not greater than n t , t ∈ [0, 1], and $l(t) = \sum\nolimits_{i \leqslant t,i \in A} {1/i,t > 0} $ . In this paper, we show that the finite-dimensional distributions of the random process $\{ Y_n (t) = (X_n (t) - l(n^t ))/\sqrt {\varrho \ln n} ,t \in [0,1]\} $ converge weakly as n → ∞ to the finite-dimensional distributions of the standard Brownian motion {W(t), t ∈ [0, 1]} in a certain class of sets A of positive asymptotic density ϱ. Pleiades Publishing, Ltd., 2013 Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 298-318 0081-5438 282:1<298 2013 282 11501 https://doi.org/10.1134/S0081543813060217 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813060217 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Yakymiv A. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 298-318 0081-5438 282:1<298 2013 282 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer