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This article has been published in Advances in Applied Mathematics (Volume 41, Issue 2, August 2008, Pages 255-264) and is available at doi:10.1016/j.aam.2007.10.001.

Errata and addenda are contained in an additional document.

Attachment: 

positivity.pdf

positivity-addendum.pdf

This is my diploma thesis, supervised by PD. dr. Ralf Gramlich, as submitted at Technische Universität Darmstadt 31 March 2008 with minor corrections.

The thesis is also available at http://arxiv.org/abs/0805.2403.

Attachment: 

diploma.pdf

This document is based on my notes taken at lectures about Gaussian random functions which were held by visiting Prof. Dr. M. Lifshits (University of St. Petersburg) at Technische Universität Darmstadt from 11 to 22 July 2005.

Attachment: 

gaussian.pdf