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Entropy 2004, 6(1), 180-215; doi:10.3390/e6010180
Article

Markov Property and Operads

1,2
1 Maphysto, Department of Mathematical Sciences, University of Aarhus, Denmark 2 Institut Elie Cartan, Faculté des Sciences, Université Henri Poincaré 54000, Vandoeuvre-les-Nancy, France
Received: 12 September 2003 / Accepted: 10 December 2003 / Published: 31 March 2004
(This article belongs to the Special Issue Quantum Limits to the Second Law of Thermodynamics)
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Abstract

We define heat kernel measure on punctured spheres. The random field which is got by this procedure is not Gaussian. We define a stochastic line bundle on the loop space, such that the punctured sphere corresponds to a generalized parallel transport on this line bundle. Markov property along the sewing loops corresponds to an operadic structure of the stochastic W.Z.N.W. model.
Keywords: random fields; stochastic integrals; W.Z.N.W. model; operads random fields; stochastic integrals; W.Z.N.W. model; operads
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Léandre, R. Markov Property and Operads. Entropy 2004, 6, 180-215.

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