Markov random fields, Markov cocycles and the 3-colored chessboard

Nishant Chandgotia, Tom Meyerovitch

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

The well-known Hammersley–Clifford Theorem states (under certain conditions) that any Markov random field is a Gibbs state for a nearest neighbor interaction. In this paper we study Markov random fields for which the proof of the Hammersley–Clifford Theorem does not apply. Following Petersen and Schmidt we utilize the formalism of cocycles for the homoclinic equivalence relation and introduce “Markov cocycles”, reparametrizations of Markov specifications. The main part of this paper exploits this to deduce the conclusion of the Hammersley–Clifford Theorem for a family of Markov random fields which are outside the theorem’s purview where the underlying graph is Zd. This family includes all Markov random fields whose support is the d-dimensional “3-colored chessboard”. On the other extreme, we construct a family of shift-invariant Markov random fields which are not given by any finite range shift-invariant interaction.

اللغة الأصليةإنجليزيّة أمريكيّة
الصفحات (من إلى)909-964
عدد الصفحات56
دوريةIsrael Journal of Mathematics
مستوى الصوت215
رقم الإصدار2
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 1 سبتمبر 2016

All Science Journal Classification (ASJC) codes

  • !!General Mathematics

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