Publication announcement: 'Random Walks, Conductance, and Resistance for the Connection Graph Laplacian'

I am excited to announce the final publication of our paper ‘Random Walks, Conductance, and Resistance for the Connection Graph Laplacian,’ written alongside Alexander Cloninger, Gal Mishne, Andreas Oslandsbotn, Zhengchao Wan, and Yusu Wang. The paper appears in SIMAX Vol. 45, No. 3, pp. 1541–1572..

We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of Dirichlet-type and Poisson-type problems on connection graphs. Additionally, we delve into random walks, taking into account both node transitions and vector rotations. This approach introduces novel concepts of effective conductance and resistance matrices for connection graphs, capturing mean rotation matrices corresponding to random walk transitions. Thereby, it provides new theoretical insights for network analysis and optimization.