On the characterization of a finite random field by conditional distribution and its Gibbs form

Linda A. Khachatryan; Boris S. Nahapetian

doi:10.1007/s10959-022-01209-6

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arXiv · 2201.09229

On the characterization of a finite random field by conditional distribution and its Gibbs form

Linda A. Khachatryan·Boris S. Nahapetian

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Abstract

In this paper, we show that the methods of mathematical statistical physics can be successfully applied to random fields in finite volumes. As a result, we obtain simple necessary and sufficient conditions for the existence and uniqueness of a finite random field with a given system of one-point conditional distributions. Using the axiomatic (without the notion of potential) definition of Hamiltonian, we show that any finite random field is Gibbsian. We also apply the proposed approach to Markov random fields.

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Linda A. Khachatryan, Boris S. Nahapetian. 2022-01-23. On the characterization of a finite random field by conditional distribution and its Gibbs form. https://doi.org/10.1007/s10959-022-01209-6

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