IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Asymptotic Behavior of Heat Kernels on Spheres of Large Dimensions

  • Voit, Michael
Registered author(s):

    Forn[greater-or-equal, slanted]2, let ([mu]x[tau], n)[tau][greater-or-equal, slanted]0be the distributions of the Brownian motion on the unit sphereSn[subset of]n+1starting in some pointx[set membership, variant]Sn. This paper supplements results of Saloff-Coste concerning the rate of convergence of[mu]x[tau], nto the uniform distributionUnonSnfor[tau]-->[infinity] depending on the dimensionn. We show that,[formula]for[tau]n:=(ln n+2s)/(2n), where erf denotes the error function. Our proof depends on approximations of the measures[mu]x[tau], nby measures which are known explicitly via Poisson kernels onSn, and which tend, after suitable projections and dilatations, to normal distributions on forn-->[infinity]. The above result as well as some further related limit results will be derived in this paper in the slightly more general context of Jacobi-type hypergroups.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.sciencedirect.com/science/article/B6WK9-45NJR18-8/2/72aba015669ca3070d8f48bf47725941
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 59 (1996)
    Issue (Month): 2 (November)
    Pages: 230-248

    as
    in new window

    Handle: RePEc:eee:jmvana:v:59:y:1996:i:2:p:230-248
    Contact details of provider: Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description

    Order Information: Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
    Web: https://shop.elsevier.com/order?id=622892&ref=622892_01_ooc_1&version=01

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:59:y:1996:i:2:p:230-248. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.