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2013
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# N. Ganikhodzhaev

P.O. Box 10, 50728, Kuala Lumpur, Malaysia
International Islamic University Malaysia

## Publications:

 Ganikhodzhaev N. N., Rozikov U. A. On quadratic stochastic operators generated by Gibbs distributions 2006, vol. 11, no. 4, pp.  467-473 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 $\mu$ 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 $\mu$ 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 $\mu$ of the Potts model converges to this measure Keywords: quadratic stochastic operator, Gibbs distribution, Potts model Citation: Ganikhodzhaev N. N., Rozikov U. A.,  On quadratic stochastic operators generated by Gibbs distributions , Regular and Chaotic Dynamics, 2006, vol. 11, no. 4, pp. 467-473 DOI:10.1070/RD2006v011n04ABEH000364