On quadratic stochastic operators
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 beh...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer
2006
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/45589/ http://irep.iium.edu.my/45589/ http://irep.iium.edu.my/45589/1/gnru-rand%282006%29.pdf |
| Summary: | 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.
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