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...
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| Format: | Article |
| Language: | English |
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Springer
2006
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| Online Access: | http://irep.iium.edu.my/45589/ http://irep.iium.edu.my/45589/1/gnru-rand%282006%29.pdf |
| _version_ | 1848782810771357696 |
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| author | Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich |
| author_facet | Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich |
| author_sort | Ganikhodjaev, Nasir |
| building | IIUM Repository |
| collection | Online Access |
| description | 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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| first_indexed | 2025-11-14T16:11:23Z |
| format | Article |
| id | iium-45589 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:11:23Z |
| publishDate | 2006 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-455892015-11-09T06:05:39Z http://irep.iium.edu.my/45589/ On quadratic stochastic operators Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich QA Mathematics 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. Springer 2006 Article PeerReviewed application/pdf en http://irep.iium.edu.my/45589/1/gnru-rand%282006%29.pdf Ganikhodjaev, Nasir and Rozikov, Utkir Abdulloevich (2006) On quadratic stochastic operators. Regular and chaotic dynamics, 11 (4). pp. 467-473. 10.1070/RD2006v011n04ABEH000364 |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich On quadratic stochastic operators |
| title | On quadratic stochastic operators |
| title_full | On quadratic stochastic operators |
| title_fullStr | On quadratic stochastic operators |
| title_full_unstemmed | On quadratic stochastic operators |
| title_short | On quadratic stochastic operators |
| title_sort | on quadratic stochastic operators |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/45589/ http://irep.iium.edu.my/45589/ http://irep.iium.edu.my/45589/1/gnru-rand%282006%29.pdf |