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The Hilbert-Galton board

Ayyer, A and Ramassamy, S (2018) The Hilbert-Galton board. In: Alea, 15 (2). pp. 755-774.

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Official URL: https://doi.org/10.30757/ALEA.v15-28


We introduce the Hilbert-Galton board as a variant of the classical Galton board. Balls fall into a row of bins at a rate depending on the bin, and at random times, each bin gets shifted one unit to the right and an empty bin is added to the left. We compute the stationary distribution of this Markov chain and show the existence of an enriched Markov chain on triangular arrays which projects down to the Hilbert-Galton board. We also define finite-ball projections of the Hilbert-Galton board, for which we compute the stationary distribution, the full spectrum and the grand coupling time. © 2018 Instituto Nacional de Matematica Pura e Aplicada.

Item Type: Journal Article
Publication: Alea
Publisher: Instituto Nacional de Matematica Pura e Aplicada
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Galton board; Markov chain; Triangle of numbers
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 03 Sep 2022 03:48
Last Modified: 03 Sep 2022 03:48
URI: https://eprints.iisc.ac.in/id/eprint/76364

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