• Login
    View Item 
    •   Home
    • Graduate Theses, Dissertations and Projects
    • Queen's Graduate Theses and Dissertations
    • View Item
    •   Home
    • Graduate Theses, Dissertations and Projects
    • Queen's Graduate Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Real Second-Order Freeness and Fluctuations of Random Matrices

    Thumbnail
    View/Open
    Redelmeier_C_Emily_I_201109_PhD.pdf (17.33Mb)
    Date
    2011-09-09
    Author
    Redelmeier, Catherine Emily Iska
    Metadata
    Show full item record
    Abstract
    We introduce real second-order freeness in second-order noncommutative probability spaces. We demonstrate that under this definition, independent ensembles of the three real models of random matrices which we consider, namely real Ginibre matrices, Gaussian orthogonal matrices, and real Wishart matrices, are asymptotically second-order free. These ensembles do not satisfy the complex definition of second-order freeness satisfied by their complex analogues. This definition may be used to calculate the asymptotic fluctuations of products of matrices in terms of the fluctuations of each ensemble.

    We use a combinatorial approach to the matrix calculations similar to genus expansion, but in which nonorientable surfaces appear, demonstrating the commonality between the real ensembles and the distinction from their complex analogues, motivating this distinct definition. We generalize the description of graphs on surfaces in terms of the symmetric group to the nonorientable case.

    In the real case we find, in addition to the terms appearing in the complex case corresponding to annular spoke diagrams, an extra set of terms corresponding to annular spoke diagrams in which the two circles of the annulus are oppositely oriented, and in which the matrix transpose appears.
    URI for this record
    http://hdl.handle.net/1974/6711
    Collections
    • Queen's Graduate Theses and Dissertations
    • Department of Mathematics and Statistics Graduate Theses
    Request an alternative format
    If you require this document in an alternate, accessible format, please contact the Queen's Adaptive Technology Centre

    DSpace software copyright © 2002-2015  DuraSpace
    Contact Us
    Theme by 
    Atmire NV
     

     

    Browse

    All of QSpaceCommunities & CollectionsPublished DatesAuthorsTitlesSubjectsTypesThis CollectionPublished DatesAuthorsTitlesSubjectsTypes

    My Account

    LoginRegister

    Statistics

    View Usage StatisticsView Google Analytics Statistics

    DSpace software copyright © 2002-2015  DuraSpace
    Contact Us
    Theme by 
    Atmire NV