## Asymptotics of products of nonnegative random matricesстатья

Информация о цитировании статьи получена из Scopus, Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 14 сентября 2013 г.
• Автор:
• Журнал: Functional Analysis and its Applications
• Том: 47
• Номер: 2
• Год издания: 2013
• Издательство: Maik Nauka/Interperiodica Publishing
• Местоположение издательства: Russian Federation
• Первая страница: 138
• Последняя страница: 147
• DOI: 10.1007/s10688-013-0018-8
• Аннотация: Asymptotic properties of products of random matrices ξ k = X k …X 1 as k → ∞ are analyzed. All product terms X i are independent and identically distributed on a finite set of nonnegative matrices A = {A 1, …, A m }. We prove that if A is irreducible, then all nonzero entries of the matrix ξ k almost surely have the same asymptotic growth exponent as k→∞, which is equal to the largest Lyapunov exponent λ(A). This generalizes previously known results on products of nonnegative random matrices. In particular, this removes all additional “nonsparsity” assumptions on matrices imposed in the literature.We also extend this result to reducible families. As a corollary, we prove that Cohen’s conjecture (on the asymptotics of the spectral radius of products of random matrices) is true in case of nonnegative matrices.
• Добавил в систему: Протасов Владимир Юрьевич

### Работа с статьей

 [1] Protasov V. Y. Asymptotics of products of nonnegative random matrices // Functional Analysis and its Applications. — 2013. — Vol. 47, no. 2. — P. 138–147. Asymptotic properties of products of random matrices ξ k = X k …X 1 as k → ∞ are analyzed. All product terms X i are independent and identically distributed on a finite set of nonnegative matrices A = {A 1, …, A m }. We prove that if A is irreducible, then all nonzero entries of the matrix ξ k almost surely have the same asymptotic growth exponent as k→∞, which is equal to the largest Lyapunov exponent λ(A). This generalizes previously known results on products of nonnegative random matrices. In particular, this removes all additional “nonsparsity” assumptions on matrices imposed in the literature.We also extend this result to reducible families. As a corollary, we prove that Cohen’s conjecture (on the asymptotics of the spectral radius of products of random matrices) is true in case of nonnegative matrices. [ DOI ]