Long range one-cookie random walk with positive speed

Andrea Collevecchio; Kais Hamza; Tuan-Minh Nguyen

doi:10.1016/j.spa.2021.08.003

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arXiv · 2011.00493

Long range one-cookie random walk with positive speed

Andrea Collevecchio·Kais Hamza·Tuan-Minh Nguyen

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Abstract

We study one-dimensional excited random walks with non-nearest neighbor 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.

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Andrea Collevecchio, Kais Hamza, Tuan-Minh Nguyen. 2020-11-01. Long range one-cookie random walk with positive speed. https://doi.org/10.1016/j.spa.2021.08.003

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