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Cubic operators corresponding to graphs. (English) Zbl 1419.47006

Summary: We introduce a notion of a cubic stochastic operator corresponding to a graph. We prove that each such operator has a unique fixed point. Besides, it is shown that any trajectory of such cubic stochastic operator exponentially rapidly converges to this fixed point.

MSC:

47H40 Random nonlinear operators
17D92 Genetic algebras
47B80 Random linear operators
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