Core Concepts
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.
Abstract
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.