On quadratic stochastic operators

Ganikhodjaev, Nasir and Rozikov, Utkir Abdulloevich (2006) On quadratic stochastic operators. Regular and chaotic dynamics, 11 (4). pp. 467-473.

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Abstract

We give a constructive description of quadratic stochastic operators which act to the set of all probability measures on some measurable space. Our construction depends on a probability measure µ and cardinality of a set of cells (configurations) which here can be finite or continual. We study behavior of trajectories of such operators for a given probability measure µ which coincides with a Gibbs measure. For the continual case we compare the quadratic operators which correspond to well-known Gibbs measures of the Potts model on Z d . These investigations allows a natural introduction of thermodynamics in studying some models of heredity. In particular, we show that any trajectory of the quadratic stochastic operator generated by a Gibbs measure µ of the Potts model converges to this measure.

Item Type:	Article (Journal)
Additional Information:	4430/45589
Uncontrolled Keywords:	quadratic stochastic operator, Gibbs distribution, Potts model
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Prof. Nasir Ganikhodjaev
Date Deposited:	09 Nov 2015 14:05
Last Modified:	09 Nov 2015 14:05
URI:	http://irep.iium.edu.my/id/eprint/45589

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