Rémi Léandre^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.
E-mail: [email protected]

Received: 12 September 2003 / Accepted: 10 December 2003 / Published: 31 March 2004

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.

MSC 2000 codes: 55P48, 60G60, 81T40, 82B31.