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/ http://irep.iium.edu.my/45589/1/gnru-rand%282006%29.pdf |
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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 |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
| collection |
Online Access |
| language |
English |
| topic |
QA Mathematics |
| spellingShingle |
QA Mathematics Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich On quadratic stochastic operators |
| 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.
|
| format |
Article |
| author |
Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich |
| author_facet |
Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich |
| author_sort |
Ganikhodjaev, Nasir |
| title |
On quadratic stochastic operators |
| title_short |
On quadratic stochastic operators |
| title_full |
On quadratic stochastic operators |
| title_fullStr |
On quadratic stochastic operators |
| title_full_unstemmed |
On quadratic stochastic operators |
| title_sort |
on quadratic stochastic operators |
| publisher |
Springer |
| publishDate |
2006 |
| 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 |
| first_indexed |
2023-09-18T21:04:51Z |
| last_indexed |
2023-09-18T21:04:51Z |
| _version_ |
1777410864437002240 |