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Doubly stochastic operators on a finite-dimensional simplex

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Abstract

Generalizing the concept of a quadratic doubly stochastic operator, we introduce the concept of an arbitrary doubly stochastic operator. We give a necessary condition for double stochasticity. Moreover, we prove an ergodic theorem for doubly stochastic operators.

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Authors and Affiliations

  1. Uzbekistan National University, Tashkent, Uzbekistan

    F. A. Shahidi

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  1. F. A. Shahidi
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Correspondence to F. A. Shahidi.

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Original Russian Text Copyright © 2009 Shahidi F. A.

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Tashkent. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 2, pp. 463–468, March–April, 2009.

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Shahidi, F.A. Doubly stochastic operators on a finite-dimensional simplex. Sib Math J 50, 368–372 (2009). https://doi.org/10.1007/s11202-009-0042-3

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  • DOI: https://doi.org/10.1007/s11202-009-0042-3

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