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...
Saved in:
| Main Authors: | , |
|---|---|
| 格式: | Article |
| 語言: | English |
| 出版: |
Springer
2006
|
| 主題: | |
| 在線閱讀: | http://irep.iium.edu.my/45589/1/gnru-rand%282006%29.pdf http://irep.iium.edu.my/45589/ |
| 標簽: |
添加標簽
沒有標簽, 成為第一個標記此記錄!
|
| 機構: | Universiti Islam Antarabangsa Malaysia |
| 語言: | English |
| 總結: | 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.
|
|---|