On the meeting of random walks on random DFA

Matteo Quattropani and Federico Sau

Stochastic Processes and their Applications, 2023, vol. 166, issue C

Abstract: We consider two random walks evolving synchronously on a random out-regular graph of n vertices with bounded out-degree r≥2, also known as a random Deterministic Finite Automaton (DFA). We show that, with high probability with respect to the generation of the graph, the meeting time of the two walks is stochastically dominated by a geometric random variable of rate (1+o(1))n−1, uniformly over their starting locations. Further, we prove that this upper bound is typically tight, i.e., it is also a lower bound when the locations of the two walks are selected uniformly at random. Our work takes inspiration from a recent conjecture by Fish and Reyzin (2017) in the context of computational learning, the connection with which is discussed.

Keywords: Random walks; Meeting times; First Visit Time Lemma; Random Deterministic Finite Automaton (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.104225

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