A Monotonicity Property for Once Reinforced Biased Random Walk on Zd

Mark Holmes, Daniel Kious

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study once-reinforced biased random walk on Zd. 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 languageEnglish
Title of host publicationSojourns in Probability Theory and Statistical Physics - III
Subtitle of host publicationInteracting Particle Systems and Random Walks, A Festschrift for Charles M. Newman
EditorsVladas Sidoravicius
Place of PublicationSingapore
PublisherSpringer Nature
Pages255-273
Number of pages19
Volume300
ISBN (Electronic)9789811503023
ISBN (Print)9789811503016
DOIs
Publication statusE-pub ahead of print - 18 Oct 2019
EventInternational Conference on Probability Theory and Statistical Physics, 2016 - Shanghai, China
Duration: 25 Mar 201627 Mar 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume300
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Probability Theory and Statistical Physics, 2016
CountryChina
CityShanghai
Period25/03/1627/03/16

Keywords

  • Coupling
  • Large bias
  • Once-reinforced random walk
  • Reinforced random walk

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Holmes, M., & Kious, D. (2019). A Monotonicity Property for Once Reinforced Biased Random Walk on Zd. 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. https://doi.org/10.1007/978-981-15-0302-3_10