Open Access
Autumn 2016 Construction of a new class of quantum Markov fields
Luigi Accardi, Farrukh Mukhamedov, Abdessatar Souissi
Adv. Oper. Theory 1(2): 206-218 (Autumn 2016). DOI: 10.22034/aot.1610.1031


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.


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Luigi Accardi. Farrukh Mukhamedov. Abdessatar Souissi. "Construction of a new class of quantum Markov fields." Adv. Oper. Theory 1 (2) 206 - 218, Autumn 2016.


Received: 13 October 2016; Accepted: 14 December 2016; Published: Autumn 2016
First available in Project Euclid: 4 December 2017

zbMATH: 1362.60065
MathSciNet: MR3723621
Digital Object Identifier: 10.22034/aot.1610.1031

Primary: 46L53
Secondary: 60J99, 46L60, 60G50, 82B10

Keywords: construction , graph , quantum Markov field , tessellation

Rights: Copyright © 2016 Tusi Mathematical Research Group

Vol.1 • No. 2 • Autumn 2016
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