On the paths Hölder continuity in models of Euclidean quantum field theory

Abstract

Sample paths properties of certain stochastic processes connected to models of Euclidean Quantum Field Theory are studied. In particular, the Hölder continuity of paths of the coordinate processes and trace processes is proven. The results are obtained by an application of classical probabilistic criteria together with basic estimates proven in Constructive Quantum Field Theory.

Acknowledgments

We are very grateful to Prof. Z. Haba and Prof. J. Zabczyk for instructive and stimulating discussions. The second author (R.G.) is grateful to the Institut Galilée, Université Paris 13 for the very kind hospitality. The financial assistance of the Polish National KBN Grant Polonium 99 is gratefully acknowledged by the second author.