Table of Contents

Conformally Invariant Random Fields and Processes — Old and New.- Diffusion Processes with Singular Dirichlet Forms.- Geometric Quantization on Wiener Manifolds.- Heat Kernels on Lie Groups.- Weak Sobolev Inequalities.- Feynman’s Functional Calculus and Shastic Calculus of Variations.- Manifolds and Graphs with Mostly Positive Curvatures.- The Thom Class of Mathai and Quillen and Probability Theory.- The General Mathematical Framework of Euclidean Quantum Mechanics: An Outline.- Naturality of Quasi-Invariance of Some Measures.- Shastic Differential Equations with Boundary Conditions.- Sobolev Inequalities and Polynomial Decay of Convolution Powers and Random Walks.- Microcanonical Distributions for One Dimensional Lattice Gases.