Advances in Operator Theory

Construction of a new class of quantum Markov fields

Luigi Accardi, Farrukh Mukhamedov, and Abdessatar Souissi

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Abstract

In the present paper, we propose a new construction of quantum Markov fields on arbitrary connected, infinite, locally finite graphs. The construction is based on a specific tessellation on the considered graph, it allows us to express the Markov property for the local structure of the graph. Our main result is the existence and uniqueness of quantum Markov field.

Article information

Source
Adv. Oper. Theory, Volume 1, Number 2 (2016), 206-218.

Dates
Received: 13 October 2016
Accepted: 14 December 2016
First available in Project Euclid: 4 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431397

Digital Object Identifier
doi:10.22034/aot.1610.1031

Mathematical Reviews number (MathSciNet)
MR3723621

Zentralblatt MATH identifier
1362.60065

Subjects
Primary: 46L53: Noncommutative probability and statistics
Secondary: 60J99, 46L60, 60G50, 82B10

Keywords
quantum Markov field graph tessellation construction

Citation

Accardi, Luigi; Mukhamedov, Farrukh; Souissi, Abdessatar. Construction of a new class of quantum Markov fields. Adv. Oper. Theory 1 (2016), no. 2, 206--218. doi:10.22034/aot.1610.1031. https://projecteuclid.org/euclid.aot/1512431397


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