Nonlocal Hamiltonian Dynamics on Sparse L\'evy Graphs: Spectral Analysis and Multimodal Sampling

Excerpt

arXiv:2610.06904v1 Announce Type: cross Abstract: We develop a sparse graph method for transporting probability mass toward multimodal target distributions through damped nonlocal Hamiltonian dynamics. The formulation combines logarithmic-mean mobility with symmetric L\'evy-type interaction weights, coupling the evolving density to an edge momentum field. A graph constructed from nearest-neighbor connections and sampled long-range edges provides direct mass exchange between spatially separated r