 Loop-erased partitioning via parametric spanning trees: Monotonicities & 1D-scalingLuca Avena, Jannetje Driessen and Twan Koperberg Stochastic Processes and their Applications, 2024, vol. 176, issue C 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. Keywords: Graph Laplacian; Random partitions; Loop-erased random walk; Spanning rooted forests; Determinantal processes (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:176:y:2024:i:c:s030441492400142x Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2024.104436 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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