 A proof of the transfer-current theorem in absence of reversibilityL. Avena and A. Gaudillière Statistics & Probability Letters, 2018, vol. 142, issue C, 17-22 Abstract: The transfer-current theorem is a well-known result in probability theory stating that edges in a uniform spanning tree of an undirected graph form a determinantal process with kernel interpretable in terms of flows. Its original derivation due to Burton and Pemantle (1993) is based on a clever induction using comparison of random walks with electrical networks. Several variants of this celebrated result have recently appeared in the literature. In this paper we give an elementary proof of an extension of this theorem when the underlying graph is directed, irreducible and finite. Further, we give a characterization of the corresponding determinantal kernel in terms of flows extending the kernel given by Burton–Pemantle to the non-reversible setting. Keywords: Finite networks; Uniform spanning tree; Spanning forests; Determinantal processes; Transfer current theorem (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:stapro:v:142:y:2018:i:c:p:17-22 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2018.06.007 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.