Long range one-cookie random walk with positive speed

Andrea Collevecchio; Kais Hamza; Tuan Minh Nguyen

doi:10.1016/j.spa.2021.08.003

Long range one-cookie random walk with positive speed

Andrea Collevecchio, Kais Hamza, Tuan Minh Nguyen

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

We study one-dimensional excited random walks with non-nearest neighbour jumps. When the process is at a vertex that has not been visited before, its next transition has a positive drift to the right, possibly with long jumps. Whenever the process visits a vertex that has already been visited in the past, its next transition is the one of a simple symmetric random walk. We give a sufficient condition for the process to have positive speed.

Original language	English
Pages (from-to)	462-478
Number of pages	17
Journal	Stochastic Processes and their Applications
Volume	142
DOIs	https://doi.org/10.1016/j.spa.2021.08.003
Publication status	Published - Dec 2021

Keywords

Excited random walks
Self-interacting random walks

Access to Document

10.1016/j.spa.2021.08.003

Cite this

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title = "Long range one-cookie random walk with positive speed",

abstract = "We study one-dimensional excited random walks with non-nearest neighbour jumps. When the process is at a vertex that has not been visited before, its next transition has a positive drift to the right, possibly with long jumps. Whenever the process visits a vertex that has already been visited in the past, its next transition is the one of a simple symmetric random walk. We give a sufficient condition for the process to have positive speed.",

keywords = "Excited random walks, Self-interacting random walks",

author = "Andrea Collevecchio and Kais Hamza and Nguyen, {Tuan Minh}",

note = "Funding Information: The authors would like to thank Burgess Davis for helpful discussions. Moreover, they thank the anonymous referees for their thorough reading and their constructive suggestions which improved the manuscript. The authors were supported by ARC, Australia grant DP180100613 . Moreover, A.C. was supported by the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers ( CE140100049 ). Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

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doi = "10.1016/j.spa.2021.08.003",

language = "English",

volume = "142",

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journal = "Stochastic Processes and their Applications",

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T1 - Long range one-cookie random walk with positive speed

AU - Collevecchio, Andrea

AU - Hamza, Kais

AU - Nguyen, Tuan Minh

N1 - Funding Information: The authors would like to thank Burgess Davis for helpful discussions. Moreover, they thank the anonymous referees for their thorough reading and their constructive suggestions which improved the manuscript. The authors were supported by ARC, Australia grant DP180100613 . Moreover, A.C. was supported by the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers ( CE140100049 ). Publisher Copyright: © 2021 Elsevier B.V.

PY - 2021/12

Y1 - 2021/12

N2 - We study one-dimensional excited random walks with non-nearest neighbour jumps. When the process is at a vertex that has not been visited before, its next transition has a positive drift to the right, possibly with long jumps. Whenever the process visits a vertex that has already been visited in the past, its next transition is the one of a simple symmetric random walk. We give a sufficient condition for the process to have positive speed.

AB - We study one-dimensional excited random walks with non-nearest neighbour jumps. When the process is at a vertex that has not been visited before, its next transition has a positive drift to the right, possibly with long jumps. Whenever the process visits a vertex that has already been visited in the past, its next transition is the one of a simple symmetric random walk. We give a sufficient condition for the process to have positive speed.

KW - Excited random walks

KW - Self-interacting random walks

UR - http://www.scopus.com/inward/record.url?scp=85116393257&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2021.08.003

DO - 10.1016/j.spa.2021.08.003

M3 - Article

AN - SCOPUS:85116393257

VL - 142

SP - 462

EP - 478

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

ER -

Long range one-cookie random walk with positive speed

Abstract

Keywords

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Other files and links

Random walks with long memory

ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights

Cite this

Long range one-cookie random walk with positive speed

Abstract

Keywords

Access to Document

Other files and links

Projects

Random walks with long memory

ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights

Cite this