Longest distance of a non-uniform dispersion process on the infinite line

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Abstract

The non-uniform dispersion process on the infinite integer line is a synchronous process where n particles are placed at the origin initially, and any particle not exclusively occupying an integer site will move at the next time step to the right adjacent integer with probability pn and to the left with probability 1− pn independently. We characterize the longest distance from the origin when the dispersion process stops, which is shown to be Θ(n) with high probability for fairly general pn.
Original languageEnglish
Article number106008
Number of pages5
JournalInformation Processing Letters
Volume164
Early online date21 Jul 2020
DOIs
Publication statusPublished - 1 Dec 2020

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