### Continuous-time digital search tree and a border aggregation model

Probability Seminar

19th May 2023, 3:30 pm – 4:30 pm

Fry Building, 2.04

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.

This is joint work with Svante Janson.

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