Decoherence for Markov chains

Abstract

The subspace generated by the eigenvectors pertaining to the peripheral spectrum of any stochastic matrix is naturally equipped with a structure of a (finite dimensional abelian) $C^{\ast }$-algebra, and the restriction of such a stochastic matrix to this subspace, indeed a $C^{\ast }$-algebra under this canonical new product, generates a conservative $C^{\ast }$-dynamical system.

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