核心概念
The authors provide an elementary proof of the correctness of the CyclePopping algorithm for efficiently sampling cycle-rooted spanning forests in weakly inconsistent U(1)-connection graphs.
摘要
The paper focuses on the CyclePopping algorithm, which is a variant of Wilson's algorithm for sampling spanning trees, and is used to efficiently sample cycle-rooted spanning forests (CRSFs) in weakly inconsistent U(1)-connection graphs.
Key highlights:
- The authors provide an elementary proof of the correctness of CyclePopping for sampling CRSFs, building on the work of Marchal on the correctness of Wilson's algorithm for sampling spanning trees.
- The proof yields the distribution of the running time of the CyclePopping algorithm, providing insights into when the algorithm is expected to run fast.
- The authors extend the proof to more general distributions over CRSFs, which are not necessarily determinantal.
- The connections to loop measures and combinatorial structures, such as pyramids of cycles, are made explicit to provide a reference for future extensions of the algorithm and its analysis.