Range and Speed of Rotor Walks on Trees

Wilfried Huss; Ecaterina Sava-Huss

doi:10.1007/s10959-019-00904-1

Range and Speed of Rotor Walks on Trees

Wilfried Huss, Ecaterina Sava-Huss^*

^*Corresponding author for this work

Institute of Discrete Mathematics (5050)

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a law of large numbers for the range of rotor walks with random initial configuration on regular trees and on Galton–Watson trees. We also show the existence of the speed for such rotor walks. More precisely, we show that on the classes of trees under consideration, even in the case when the rotor walk is recurrent, the range grows at linear speed.

Original language	English
Pages (from-to)	1657-1690
Number of pages	34
Journal	Journal of Theoretical Probability
Volume	33
Issue number	3
DOIs	https://doi.org/10.1007/s10959-019-00904-1
Publication status	Published - 1 Sep 2020

Keywords

Contour function
Galton–Watson tree
Generating function
Law of large numbers
Range
Rate of escape
Recurrence
Rotor walk
Transience

ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Statistics, Probability and Uncertainty

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10.1007/s10959-019-00904-1

Cite this

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abstract = "We prove a law of large numbers for the range of rotor walks with random initial configuration on regular trees and on Galton–Watson trees. We also show the existence of the speed for such rotor walks. More precisely, we show that on the classes of trees under consideration, even in the case when the rotor walk is recurrent, the range grows at linear speed.",

keywords = "Contour function, Galton–Watson tree, Generating function, Law of large numbers, Range, Rate of escape, Recurrence, Rotor walk, Transience",

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AB - We prove a law of large numbers for the range of rotor walks with random initial configuration on regular trees and on Galton–Watson trees. We also show the existence of the speed for such rotor walks. More precisely, we show that on the classes of trees under consideration, even in the case when the rotor walk is recurrent, the range grows at linear speed.

KW - Contour function

KW - Galton–Watson tree

KW - Generating function

KW - Law of large numbers

KW - Range

KW - Rate of escape

KW - Recurrence

KW - Rotor walk

KW - Transience

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ER -

Range and Speed of Rotor Walks on Trees

Abstract

Keywords

ASJC Scopus subject areas

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