Continuous time digital search tree and a border aggregation model

DOI10.3150/21-BEJ1429zbMATH Open1507.60133arXiv2004.13957MaRDI QIDQ6339636

Publication date: 29 April 2020

Abstract: We consider the continuous-time version of the random digital search tree, and construct a coupling with a border aggregation model as studied in Thacker and Volkov (2018), showing a relation between the height of the tree and the time required for aggregation. This relation carries over to the corresponding discrete-time models. As a consequence we find a very precise asymptotic result for the time to aggregation, using recent results by Drmota et al. (2020) for the digital search tree.

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Combinatorial probability (60C05)

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