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Asymptotics of entries of products of nonnegative 2-by-2 matrices
- Publication Year :
- 2021
-
Abstract
- Let $M$ and $M_n,n\ge1$ be nonnegative 2-by-2 matrices such that $\lim_{n\rightarrow\infty}M_n=M.$ It is usually hard to estimate the entries of $M_{k+1}\cdots M_{k+n}$ which are useful in many applications. In this paper, under a mild condition, we show that up to a multiplication of some positive constants, entries of $M_{k+1}\cdots M_{k+n}$ are asymptotically the same as $\xi_{k+1}\cdots \xi_{k+n},$ the product of the tails of a continued fraction which is related to the matrices $M_k,k\ge1,$ as $n\rightarrow\infty.$<br />Comment: 14 pages; we add some new results in this edition
- Subjects :
- Mathematics - Combinatorics
Primary 15B48, Secondary 11A55
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2111.10232
- Document Type :
- Working Paper