Random covers of finite homogeneous lattices

• Дата: 2006
• Автор: Alekseychuk, A.N.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2006
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/4437
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: 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.