Mathematical Models for Transport in Macroscopic and Mesoscopic Systems - Abstract

Post, Olaf

Generalised discrete Laplacians and quantum graphs

In this talk, we define a generalisation of the discrete Laplace operator on a combinatorial graph. These generalised Laplacians appear in a natural way from the spectral analysis of quantum graph Laplacians with general vertex boundary conditions. In the case of the standard (“Kirchhoff”) boundary conditions, the discrete operator is the usual combinatorial Laplacian. We also comment on trace formulas.