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kappa-cut on paths and some trees
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
McGill Univ, Montreal, PQ, Canada.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2019 (English)In: Electronic Journal of Probability, ISSN 1083-6489, E-ISSN 1083-6489, Vol. 24, no 53Article in journal (Refereed) Published
Abstract [en]

We define the (random) kappa-cut number of a rooted graph to model the difficulty of the destruction of a resilient network. The process is as the cut model of Meir and Moon [21] except now a node must be cut kappa times before it is destroyed. The first order terms of the expectation and variance of chi(n), the kappa-cut number of a path of length n, are proved. We also show that chi(n), after rescaling, converges in distribution to a limit B-kappa, which has a complicated representation. The paper then briefly discusses the kappa-cut number of some trees and general graphs. We conclude by some analytic results which may be of interest.

Place, publisher, year, edition, pages
UNIV WASHINGTON, DEPT MATHEMATICS , 2019. Vol. 24, no 53
Keywords [en]
cutting, kappa-cut, random trees
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-390273DOI: 10.1214/19-EJP318ISI: 000472651200001OAI: oai:DiVA.org:uu-390273DiVA, id: diva2:1341268
Funder
Knut and Alice Wallenberg FoundationSwedish Research CouncilRagnar Söderbergs stiftelseAvailable from: 2019-08-08 Created: 2019-08-08 Last updated: 2019-08-08Bibliographically approved

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