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Algebraic random walks in the setting of symmetric functions

Jarvis, PD ORCID: 0000-0002-5330-6789 and Ellinas, D 2017 , 'Algebraic random walks in the setting of symmetric functions' , Reports on Mathematical Physics, vol. 79, no. 3 , pp. 347-366 , doi: 10.1016/S0034-4877(17)30048-4.

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Using the standard formulation of algebraic random walks (ARWs) via coalgebras, we consider ARWs for co- and Hopf-algebraic structures in the ring of symmetric functions. These derive from different types of products by dualisation, giving the dual pairs of outer multiplication and outer coproduct, inner multiplication and inner coproduct, and symmetric function plethysm and plethystic coproduct. Adopting standard coordinates for a class of measures (and corresponding distribution functions) to guarantee positivity and correct normalisation, we show the effect of appropriate walker steps of the outer, inner and plethystic ARWs. If the coordinates are interpreted as heights or occupancies of walker(s) at different locations, these walks introduce translations, dilations (scalings) and inflations of the height coordinates, respectively.

Item Type: Article
Authors/Creators:Jarvis, PD and Ellinas, D
Keywords: plethysm, Hopf algebras, random walks, algebraic combinatorics
Journal or Publication Title: Reports on Mathematical Physics
Publisher: Pergamon-Elsevier Science Ltd
ISSN: 0034-4877
DOI / ID Number: 10.1016/S0034-4877(17)30048-4
Copyright Information:

Copyright 2017 Polish Scientific Publishers

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