Balanced Excited Random Walk in Two Dimensions
Omer Angel, Mark Holmes, Alejandro Ram\'irez
TL;DR
This paper establishes new bounds on the range of the Balanced Excited Random Walk in two dimensions, confirming a conjecture and providing the first significant results for this model in 2D.
Contribution
It provides the first non-trivial bounds for the 2D Balanced Excited Random Walk and verifies a conjecture by Benjamini, Kozma, and Schapira.
Findings
Established upper and lower bounds on the walk's range
Verified a conjecture in the field
First non-trivial results for this model in two dimensions
Abstract
We give non-trivial upper and lower bounds on the range of the so-called Balanced Excited Random Walk in two dimensions, and verify a conjecture of Benjamini, Kozma and Schapira. To the best of our knowledge these are the first non-trivial results for this 2-dimensional model
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Markov Chains and Monte Carlo Methods