Book Chapter

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

Mark Holmes, Daniel Kious

Springer Proceedings in Mathematics and Statistics | SPRINGER-VERLAG SINGAPORE PTE LTD | Published : 2019


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.

University of Melbourne Researchers


Awarded by Australian Research Council

Funding Acknowledgements

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 Polytechnique F ' ed ' erale de Lausanne (EPFL) to which he was affiliated to at the time this work was partly done.