Long range one-cookie random walk with positive speed

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1 Citation (Scopus)


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

Original languageEnglish
Pages (from-to)462-478
Number of pages17
JournalStochastic Processes and their Applications
Publication statusPublished - Dec 2021


  • Excited random walks
  • Self-interacting random walks

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