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Long range one-cookie random walk with positive speed
Andrea Collevecchio, Kais Hamza, Tuan-Minh Nguyen · 2020-11-01 · via math.PR updates on arXiv.org

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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