Nonlocal Hamiltonian Dynamics on Sparse Lévy Graphs: Spectral Analysis and Multimodal Sampling
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 Lévy-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 regions. Once the graph is constructed, the density evolution is deterministic, and each update costs linear in the number of nodes and the long-range sampling budget. Linearization around the target distribution yields a damped oscillator governed b...
| Authors | Miaolei Zheng, Ting Gao, Jinqiao Duan |
|---|---|
| Primary category | math.DS |
| Published | 1 October 2026 |
| Last updated at source | 1 October 2026 |
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