Spectral Geometry of Graphs

The spectral geometry of infinite graphs deals with three major themes and their interplay: the spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with its probabilistic aspects. In this book, all three themes are brought together coherently under the perspective of Dirichlet forms, providing a powerful and unified approach.

Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis.