Excited random walk in two dimensions has linear speed
Gady Kozma
TL;DR
This paper proves that in two dimensions, excited random walk exhibits a linear drift to the right over time, demonstrating a consistent directional bias in this stochastic process.
Contribution
The paper establishes the linear speed of excited random walk in two dimensions, providing a rigorous proof of its persistent rightward drift.
Findings
Excited random walk in 2D drifts linearly over time.
The process exhibits a persistent rightward bias.
Theoretical proof of linear speed in 2D excited random walk.
Abstract
Excited random walk is a process that has a drift to the right whenever it encounters a new vertex. The paper shows that in two dimensions it drifts to the right linearly in time.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Cold Atom Physics and Bose-Einstein Condensates · Advanced Thermodynamics and Statistical Mechanics