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VOL. 7 | 2006 Quantum Groups and Stohastic Models


The aim of this paper is to show that stochastic models provide a very good playground to enhance the utility of quantum groups. Quantum groups arise naturally and the deformation parameter has a direct physical meaning for diffusion systems where it is just the ratio of left/right probability rate. In the matrix product state approach to diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra which defines a noncommutative space with a quantum group action as its symmetry. Boundary processes amount for the appearance of parameter-dependent linear terms in the algebra which leads to a reduction of the bulk symmetry.


Published: 1 January 2006
First available in Project Euclid: 13 July 2015

zbMATH: 1098.81048
MathSciNet: MR2228363

Digital Object Identifier: 10.7546/giq-7-2006-57-78

Rights: Copyright © 2006 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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