A rotor configuration on a graph contains in every vertex an infinite ordered sequence of rotors, each is pointing to a neighbor of the vertex. After sampling a configuration according to some probability measure, a rotor walk is a deterministic process: at each step it chooses the next unused rotor in its current location, and uses it to jump to the neighboring vertex to which it points. Rotor walks capture many aspects of the expected behavior of simple random walks. However, this similarity breaks down for the property of having an infinite excursion. In this paper we study that question for natural random configuration models on regular trees. Our results suggest that in this context the rotor model behaves like the simple random walk unless it is not “close to” the standard rotor-router model.

Muller, S., Orenshtein, T. (2017). Infinite excursions of rotor walks on regular trees. ELECTRONIC JOURNAL OF COMBINATORICS, 24(2) [10.37236/5781].

Infinite excursions of rotor walks on regular trees

Orenshtein T.
2017

Abstract

A rotor configuration on a graph contains in every vertex an infinite ordered sequence of rotors, each is pointing to a neighbor of the vertex. After sampling a configuration according to some probability measure, a rotor walk is a deterministic process: at each step it chooses the next unused rotor in its current location, and uses it to jump to the neighboring vertex to which it points. Rotor walks capture many aspects of the expected behavior of simple random walks. However, this similarity breaks down for the property of having an infinite excursion. In this paper we study that question for natural random configuration models on regular trees. Our results suggest that in this context the rotor model behaves like the simple random walk unless it is not “close to” the standard rotor-router model.
Articolo in rivista - Articolo scientifico
Multi-type branching process; Recurrence; Regular tree; Rotor walk; Self interacting walk; Transience;
English
2017
24
2
#P2.18
none
Muller, S., Orenshtein, T. (2017). Infinite excursions of rotor walks on regular trees. ELECTRONIC JOURNAL OF COMBINATORICS, 24(2) [10.37236/5781].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/362322
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