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Algebraic random walks in the setting of symmetric functions

Citation

Jarvis, PD and Ellinas, D, Algebraic random walks in the setting of symmetric functions, Reports on Mathematical Physics, 79, (3) pp. 347-366. ISSN 0034-4877 (2017) [Refereed Article]

Copyright Statement

Copyright 2017 Polish Scientific Publishers

DOI: doi:10.1016/S0034-4877(17)30048-4

Abstract

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 Details

Item Type:Refereed Article
Keywords:plethysm, Hopf algebras, random walks, algebraic combinatorics
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Operator Algebras and Functional Analysis
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:124324
Year Published:2017
Deposited By:Mathematics and Physics
Deposited On:2018-02-19
Last Modified:2018-04-30
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