Random covers of finite homogeneous lattices

• Datum: 2006
• ISSN: 0321-3900
• 1. Verfasser: Alekseychuk, A.N.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2006
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/4437
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Random covers of finite homogeneous lattices / A.N. Alekseychuk // Theory of Stochastic Processes. — 2006. — Т. 12 (28), № 1-2. — С. 12–19. — Бібліогр.: 10 назв.— англ.

We develop and extend some results for the scheme of independent random elements
 distributed on a finite lattice. In particular, we introduce the concept of the cover of
 a homogeneous lattice Ln of rank n and derive the exact equations and estimations
 for the number of covers with a given number of blocks and for the total covers
 number of the lattice Ln. A theorem about the asymptotic normality of the blocks
 number in a random equiprobable cover of the lattice Ln is proved. The concept of
 the cover index of the lattice Ln, that extend the notion of the cover index of a finite
 set by its independent random subsets, is introduced. Applying the lattice moments
 method, the limit distribution as n→∞ for the cover index of a subspace lattice of
 the n-dimensional vector space over a finite field is determined.