MURAL - Maynooth University Research Archive Library

    Coefficients of ergodicity and the scrambling index

    Akelbek, Mahmud and Kirkland, Steve (2009) Coefficients of ergodicity and the scrambling index. Linear Algebra and its Applications, 430 (4). pp. 1111-1130. ISSN 0024-3795

    [img] Download (364kB)

    Share your research

    Twitter Facebook LinkedIn GooglePlus Email more...

    Add this article to your Mendeley library


    For a primitive stochastic matrix S, upper bounds on the second largest modulus of an eigenvalue of S are very important, because they determine the asymptotic rate of convergence of the sequence of powers of the corresponding matrix. In this paper, we introduce the definition of the scrambling index for a primitive digraph. The scrambling index of a primitive digraph D is the smallest positive integer k such that for every pair of vertices u and v, there is a vertex w such that we can get to w from u and v in D by directed walks of length k; it is denoted by k(D).We investigate the scrambling index for primitive digraphs, and give an upper bound on the scrambling index of a primitive digraph in terms of the order and the girth of the digraph. By doing so we provide an attainable upper bound on the second largest modulus of eigenvalues of a primitive matrix that make use of the scrambling index.

    Item Type: Article
    Keywords: Scrambling index; Primitive digraph; Coefficient of ergodicity;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 2060
    Depositing User: Professor Steve Kirkland
    Date Deposited: 21 Jul 2010 13:53
    Journal or Publication Title: Linear Algebra and its Applications
    Publisher: Elsevier
    Refereed: Yes
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

    Repository Staff Only(login required)

    View Item Item control page


    Downloads per month over past year

    Origin of downloads