Journal article
On strict monotonicity of the speed for excited random walks in one dimension
M Holmes
Electronic Communications in Probability | UNIV WASHINGTON, DEPT MATHEMATICS | Published : 2015
DOI: 10.1214/ECP.v20-4212
Abstract
We give a “direct” coupling proof of strict monotonicity of the speed for 1-dimensional multi-excited random walks with positive speed. This reproves (and extends) a recent result of Peterson without using branching processes.
Grants
Funding Acknowledgements
This work is supported in part by the Marsden Fund, administered by RSNZ. The author thanks the referee for helpful comments that lead to improvements in the final version of the paper. The author also thanks Elena Kosygina, Tom Salisbury, and Gady Kozma for helpful discussions.