IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v190y2025ics0304414925001668.html

Renewal structure of the tree builder random walk

Author

Listed:
  • Ribeiro, Rodrigo

Abstract

In this paper, we study a class of random walks that build their own tree. At each step, the walker attaches a random number of leaves to its current position. The model can be seen as a subclass of the Random Walk in Changing Environments (RWCE) introduced by G. Amir, I. Benjamini, O. Gurel-Gurevich and G. Kozma. We develop a renewal framework for the process analogous to that established by A-S. Sznitman and M. Zerner in the context of RWRE. This provides a more robust foundation for analyzing the model. As a result of our renewal framework, we establish several limit theorems for the walker’s distance, which include the Strong Law of Large Numbers (SLLN), the Law of the Iterated Logarithm (LIL), Central Limit Theorem (CLT) and Invariance Principle, under an i.i.d. hypothesis for the walker’s leaf-adding mechanism. Further, we show that the limit speed defined by the SLLN is a continuous function over the space of probability distributions on N.

Suggested Citation

  • Ribeiro, Rodrigo, 2025. "Renewal structure of the tree builder random walk," Stochastic Processes and their Applications, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:spapps:v:190:y:2025:i:c:s0304414925001668
    DOI: 10.1016/j.spa.2025.104725
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414925001668
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104725?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    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:eee:spapps:v:190:y:2025:i:c:s0304414925001668. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.