IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-44479-6_29.html
   My bibliography  Save this book chapter

First Order Probabilities for Galton–Watson Trees

In: A Journey Through Discrete Mathematics

Author

Listed:
  • Moumanti Podder

    (New York University, Courant Institute of Mathematical Sciences)

  • Joel Spencer

    (New York University, Computer Science and Mathematics Departments, Courant Institute of Mathematical Sciences)

Abstract

In the regime of Galton–Watson trees, first order logic statements are roughly equivalent to examining the presence of specific finite subtrees. We consider the space of all trees with Poisson offspring distribution and show that such finite subtrees will be almost surely present when the tree is infinite. Introducing the notion of universal trees, we show that all first order sentences of quantifier depth k depend only on local neighbourhoods of the root of sufficiently large radius depending on k. We compute the probabilities of these neighbourhoods conditioned on the tree being infinite. We give an almost sure theory for infinite trees.

Suggested Citation

  • Moumanti Podder & Joel Spencer, 2017. "First Order Probabilities for Galton–Watson Trees," Springer Books, in: Martin Loebl & Jaroslav Nešetřil & Robin Thomas (ed.), A Journey Through Discrete Mathematics, pages 711-734, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-44479-6_29
    DOI: 10.1007/978-3-319-44479-6_29
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-319-44479-6_29. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.