GROWTH EXPONENT FOR LOOP-ERASED RANDOM WALK IN THREE DIMENSIONS

GROWTH EXPONENT FOR LOOP-ERASED RANDOM WALK IN THREE DIMENSIONS

Let Mn be the number of steps of the loop-erasure of a simple random walk on ℤ³ run until its first exit from a ball of radius n. In the paper, we will show the existence of the growth exponent, that is, we show that there exists β > 0 such that lim lim n → ∞ log E ( M n ) log n = β .

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:The Annals of probability 2018-03, Vol.46 (2), p.687-774
1. Verfasser: Shiraishi, Daisuke
Format: Artikel
Sprache:eng
Schlagworte:
Random walk
Random walk theory
Studies
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Let Mn be the number of steps of the loop-erasure of a simple random walk on ℤ³ run until its first exit from a ball of radius n. In the paper, we will show the existence of the growth exponent, that is, we show that there exists β > 0 such that lim lim n → ∞ log E ( M n ) log n = β .
ISSN:0091-1798
2168-894X
DOI:10.1214/16-aop1165