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Stochastic Processes and their Applications
Article
License: Elsevier Non-Commercial
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Stochastic Processes and their Applications
Article . 2016 . Peer-reviewed
License: Elsevier Non-Commercial
Data sources: Crossref
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https://dx.doi.org/10.48550/ar...
Article . 2013
License: arXiv Non-Exclusive Distribution
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Excited Mob

Authors: Amir G.; Orenshtein T.;
Abstract

We show that for an i.i.d. bounded and weakly elliptic cookie environment, one dimensional excited random walk on the $k$-time leftover environment is right transient if and only if $��> k+1$ and has positive speed if and only if $��> k+2$, where $��$ is the expected drift per site. This gives, to the best of our knowledge, the first example of an environment with positive speed that has stationary and ergodic properties but does not follow by trivial comparison to an i.i.d. environment. In another formulation, we show that on such environments an excited mob of $k$ walkers is right transient if and only if $��> k$ and moves with positive speed if and only if $��>k+1$. We show that for stationary and erogodic cookie environments, a law of large numbers for the walkers on leftover environments holds. Whenever the environments are also elliptic, a zero-one law for directional transience is also proven.

V2 includes minor fixes + a new section on stationary leftover environments

Country
Italy
Keywords

Probability (math.PR), FOS: Mathematics, Abelianness; Cookie walk; Excited random walk; Law of large numbers; Limit theorems; Random environment; Recurrence; Regeneration structure; Transience; Zero one laws;, Mathematics - Probability

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green
hybrid