Generalisation of the Hammersley-Clifford theorem on bipartite graphs-Reference-Cited by-同舟云学术

Generalisation of the Hammersley-Clifford theorem on bipartite graphs

Published:2017-05-01 Issue:10 Volume:369 Page:7107-7137
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Chandgotia Nishant

Abstract

The Hammersley-Clifford theorem states that if the support of a Markov random field has a safe symbol, then it is a Gibbs state with some nearest neighbour interaction. In this paper we generalise the theorem with an added condition that the underlying graph is bipartite. Taking inspiration from Brightwell and Winkler (J. Combin. Theory Ser. B 78 (2000), 141–166) we introduce a notion of folding for configuration spaces called strong config-folding proving that if all Markov random fields supported on X X are Gibbs with some nearest neighbour interaction, then so are Markov random fields supported on the ‘strong config-folds’ and ‘strong config-unfolds’ of X X .

Funder

Faculty of Graduate Studies, University of British Columbia

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/tran/2017-369-10/S0002-9947-2017-06899-9/tran6899_AM.pdf

Reference15 articles.

1. Gibbs measures and dismantlable graphs;Brightwell, Graham R.;J. Combin. Theory Ser. B,2000

2. Markov random fields and measures with nearest neighbour potentials;Nishant Chandgotia;MSc Thesis,2011

3. Four-cycle free graphs, height functions, the pivot property and entropy minimality;Nishant Chandgotia;Ergodic Theory Dynam. Systems (Accepted),2015

4. One-dimensional Markov random fields, Markov chains and topological Markov fields;Chandgotia, Nishant;Proc. Amer. Math. Soc.,2014

5. Markov random fields, Markov cocycles and the 3-colored chessboard;Chandgotia, Nishant;Israel J. Math.,2016

Cited by 25 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Automatic Segmentation Method for the Nuclei Contour of High Resolution Rat Brain;Proceedings of the 2023 6th International Conference on Big Data Technologies;2023-09-22

2. Gibbsian Representations of Continuous Specifications: The Theorems of Kozlov and Sullivan Revisited;Communications in Mathematical Physics;2021-02-11

3. Index;An Introduction to Symbolic Dynamics and Coding;2021-01-21

4. Notation Index;An Introduction to Symbolic Dynamics and Coding;2021-01-21

5. Addendum Bibliography;An Introduction to Symbolic Dynamics and Coding;2021-01-21