This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform Log-Sobolev inequality.

Provides an approach to the problem of multiplicity and global bifurcation of semilinear elliptic equations, demonstrating applications of modern bifurcation theory to important nonlinear equations in physics, chemistry and biology. This volume presents theory of precise bifurcation diagrams for the development of radially symmetric solutions.