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Entropy 2004, 6(1), 180-215; doi:10.3390/e6010180
Markov Property and Operads
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)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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