 Renewal structure of the tree builder random walkRodrigo Ribeiro Stochastic Processes and their Applications, 2025, vol. 190, issue C 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. Date: 2025 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:190:y:2025:i:c:s0304414925001668 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2025.104725 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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