Random walks, conductance, and resistance for the connection graph Laplacian (Q6592220)

The paper studies random walks, conductance, and resistance for the connection graph Laplacian. It considers the analysis of Dirichlet problems and random walks on connection graphs. The connections of the resistance matrix for connection graphs to random walks and the Dirichlet problem are explored. A scalar version of effective resistance is proposed for connection graphs, stressing its continuity with respect to changes in the underlying signature. The paper extends Dirichlet problems to connection graphs and establishes several fundamental properties including the maximum norm principle. It defines effective resistance and effective conductance on connection graphs generalizing classical definitions.