Gibbs Fields (Basic Notions)

1991 ◽  
pp. 1-26
Author(s):  
V. A. Malyshev ◽  
R. A. Minlos
Keyword(s):  
Gibbs Fields

Gibbs fields

1994 ◽  
pp. 63-73
Author(s):  
Paul Doukhan
Keyword(s):  
Gibbs Fields

scholarly journals Compactness and the maximal Gibbs state for random Gibbs fields on a lattice

1982 ◽  
Vol 84 (3) ◽  
pp. 297-327 ◽  
Author(s):  
Jean Bellissard ◽  
Raphael H�egh-Krohn
Keyword(s):  
Gibbs State ◽  
Gibbs Fields

scholarly journals The Gibbs fields approach and related dynamics in image processing

2008 ◽  
Vol 11 (2) ◽  
pp. 293 ◽  
Author(s):  
Descombes ◽  
Zhizhina
Keyword(s):  
Image Processing ◽  
Gibbs Fields

scholarly journals On a Class of Tensor Markov Fields

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 451
Author(s):  
Enrique Hernández-Lemus
Keyword(s):  
Graphical Models ◽  
Random Fields ◽  
Markov Random Fields ◽  
Random Variables ◽  
Probability Measures ◽  
Gibbs Fields ◽  
Markov Random ◽  
Statistical Dependency ◽  
Markov Fields ◽  
Dependency Structures

Here, we introduce a class of Tensor Markov Fields intended as probabilistic graphical models from random variables spanned over multiplexed contexts. These fields are an extension of Markov Random Fields for tensor-valued random variables. By extending the results of Dobruschin, Hammersley and Clifford to such tensor valued fields, we proved that tensor Markov fields are indeed Gibbs fields, whenever strictly positive probability measures are considered. Hence, there is a direct relationship with many results from theoretical statistical mechanics. We showed how this class of Markov fields it can be built based on a statistical dependency structures inferred on information theoretical grounds over empirical data. Thus, aside from purely theoretical interest, the Tensor Markov Fields described here may be useful for mathematical modeling and data analysis due to their intrinsic simplicity and generality.

The uniqueness regime of Gibbs fields with unbounded disorder

1995 ◽  
Vol 81 (3-4) ◽  
pp. 829-835 ◽  
Author(s):  
G. Gielis ◽  
C. Maes
Keyword(s):  
Gibbs Fields
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