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Loop-erased partitioning via parametric spanning trees: Monotonicities & 1D-scaling

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  • Avena, Luca
  • Driessen, Jannetje
  • Koperberg, Twan

Abstract

We consider a parametric version of the UST (Uniform Spanning Tree) measure on arbitrary directed weighted finite graphs with tuning (killing) parameter q>0. This is obtained by considering the standard random weighted spanning tree on the extended graph built by adding a ghost state † and directed edges to it, of constant weights q, from any vertex of the original graph. The resulting measure corresponds to a random spanning rooted forest of the graph where the parameter q tunes the intensity of the number of trees as follows: partitions with many trees are favored for q>1, while as q→0, the standard UST of the graph is recovered. We are interested in the behavior of the induced random partition, referred to as Loop-erased partitioning, which gives a correlated cluster model, as the multiscale parameter q∈[0,∞) varies.

Suggested Citation

  • Avena, Luca & Driessen, Jannetje & Koperberg, Twan, 2024. "Loop-erased partitioning via parametric spanning trees: Monotonicities & 1D-scaling," Stochastic Processes and their Applications, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:spapps:v:176:y:2024:i:c:s030441492400142x
    DOI: 10.1016/j.spa.2024.104436
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    References listed on IDEAS

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    1. Avena, L. & Gaudillière, A., 2018. "A proof of the transfer-current theorem in absence of reversibility," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 17-22.
    2. L. Avena & A. Gaudillière, 2018. "Two Applications of Random Spanning Forests," Journal of Theoretical Probability, Springer, vol. 31(4), pages 1975-2004, December.
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