A Monotonicity Property for Once Reinforced Biased Random Walk on Zd

Mark Holmes; Daniel Kious

doi:10.1007/978-981-15-0302-3_10

A Monotonicity Property for Once Reinforced Biased Random Walk on Z^d

University of Melbourne

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Abstract

We study once-reinforced biased random walk on Z^d. We prove that for sufficiently large bias, the speed v(β) is monotone decreasing in the reinforcement parameter β in the region [0,β₀], where β₀ is a small parameter depending on the underlying bias. This result is analogous to results on Galton–Watson trees obtained by Collevecchio and the authors.

Original language	English
Title of host publication	Sojourns in Probability Theory and Statistical Physics - III
Subtitle of host publication	Interacting Particle Systems and Random Walks, A Festschrift for Charles M. Newman
Editors	Vladas Sidoravicius
Place of Publication	Singapore
Publisher	Springer Nature
Pages	255-273
Number of pages	19
Volume	300
ISBN (Electronic)	9789811503023
ISBN (Print)	9789811503016
DOIs	https://doi.org/10.1007/978-981-15-0302-3_10
Publication status	E-pub ahead of print - 18 Oct 2019
Event	International Conference on Probability Theory and Statistical Physics, 2016 - Shanghai, China Duration: 25 Mar 2016 → 27 Mar 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	300
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Probability Theory and Statistical Physics, 2016
Country/Territory	China
City	Shanghai
Period	25/03/16 → 27/03/16

Funding

This research was supported under Australian Research Council?s Discovery Programme (Future Fellowship project number FT160100166). DK is grateful to the University of Auckland for their hospitality and to the Ecole Polytech-nique F?d?rale de Lausanne (EPFL) to which he was affiliated to at the time this work was partly done.

Keywords

Coupling
Large bias
Once-reinforced random walk
Reinforced random walk

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-981-15-0302-3_10

https://link.springer.com/chapter/10.1007/978-981-15-0302-3_10

Cite this

Holmes, M., & Kious, D. (2019). A Monotonicity Property for Once Reinforced Biased Random Walk on Z^d. In V. Sidoravicius (Ed.), Sojourns in Probability Theory and Statistical Physics - III: Interacting Particle Systems and Random Walks, A Festschrift for Charles M. Newman (Vol. 300, pp. 255-273). (Springer Proceedings in Mathematics and Statistics; Vol. 300). Springer Nature. Advance online publication. https://doi.org/10.1007/978-981-15-0302-3_10

A Monotonicity Property for Once Reinforced Biased Random Walk on Z^d. / Holmes, Mark; Kious, Daniel.
Sojourns in Probability Theory and Statistical Physics - III: Interacting Particle Systems and Random Walks, A Festschrift for Charles M. Newman. ed. / Vladas Sidoravicius. Vol. 300 Singapore: Springer Nature, 2019. p. 255-273 (Springer Proceedings in Mathematics and Statistics; Vol. 300).

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Holmes, M & Kious, D 2019, A Monotonicity Property for Once Reinforced Biased Random Walk on Z^d. in V Sidoravicius (ed.), Sojourns in Probability Theory and Statistical Physics - III: Interacting Particle Systems and Random Walks, A Festschrift for Charles M. Newman. vol. 300, Springer Proceedings in Mathematics and Statistics, vol. 300, Springer Nature, Singapore, pp. 255-273, International Conference on Probability Theory and Statistical Physics, 2016, Shanghai, China, 25/03/16. https://doi.org/10.1007/978-981-15-0302-3_10

Holmes M, Kious D. A Monotonicity Property for Once Reinforced Biased Random Walk on Z^d. In Sidoravicius V, editor, Sojourns in Probability Theory and Statistical Physics - III: Interacting Particle Systems and Random Walks, A Festschrift for Charles M. Newman. Vol. 300. Singapore: Springer Nature. 2019. p. 255-273. (Springer Proceedings in Mathematics and Statistics). Epub 2019 Oct 18. doi: 10.1007/978-981-15-0302-3_10

Holmes, Mark ; Kious, Daniel. / A Monotonicity Property for Once Reinforced Biased Random Walk on Z^d. Sojourns in Probability Theory and Statistical Physics - III: Interacting Particle Systems and Random Walks, A Festschrift for Charles M. Newman. editor / Vladas Sidoravicius. Vol. 300 Singapore : Springer Nature, 2019. pp. 255-273 (Springer Proceedings in Mathematics and Statistics).

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