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2019 Upper and lower bounds on the speed of a one-dimensional excited random walk
Erin Madden, Brian Kidd, Owen Levin, Jonathon Peterson, Jacob Smith, Kevin M. Stangl
Involve 12(1): 97-115 (2019). DOI: 10.2140/involve.2019.12.97

Abstract

An excited random walk (ERW) is a self-interacting non-Markovian random walk in which the future behavior of the walk is influenced by the number of times the walk has previously visited its current site. We study the speed of the walk, defined as V= limn(Xnn), where Xn is the state of the walk at time n. While results exist that indicate when the speed is nonzero, there exists no explicit formula for the speed. It is difficult to solve for the speed directly due to complex dependencies in the walk since the next step of the walker depends on how many times the walker has reached the current site. We derive the first nontrivial upper and lower bounds for the speed of the walk. In certain cases these upper and lower bounds are remarkably close together.

Citation

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Erin Madden. Brian Kidd. Owen Levin. Jonathon Peterson. Jacob Smith. Kevin M. Stangl. "Upper and lower bounds on the speed of a one-dimensional excited random walk." Involve 12 (1) 97 - 115, 2019. https://doi.org/10.2140/involve.2019.12.97

Information

Received: 10 July 2017; Revised: 9 November 2017; Accepted: 10 December 2017; Published: 2019
First available in Project Euclid: 26 October 2018

zbMATH: 1391.60239
MathSciNet: MR3810481
Digital Object Identifier: 10.2140/involve.2019.12.97

Subjects:
Primary: 60K35
Secondary: 60G50

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 1 • 2019
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