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Träfflista för sökning "WFRF:(Wästlund Johan) ;pers:(Janson Svante)"

Sökning: WFRF:(Wästlund Johan) > Janson Svante

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1.
  • Holroyd, Alexander E., et al. (författare)
  • Minimal matchings of point processes
  • 2022
  • Ingår i: Probability Theory and Related Fields. - : Springer Science and Business Media LLC. - 0178-8051 .- 1432-2064. ; 184:1-2, s. 571-611
  • Tidskriftsartikel (refereegranskat)abstract
    • Suppose that red and blue points form independent homogeneous Poisson processes of equal intensity in R-d. For a positive (respectively, negative) parameter gamma we consider red-blue matchings that locally minimize (respectively, maximize) the sum of gamma th powers of the edge lengths, subject to locally minimizing the number of unmatched points. The parameter can be viewed as a measure of fairness. The limit gamma -> -infinity is equivalent to Gale-Shapley stable matching. We also consider limits as gamma approaches 0, 1-, 1+ and infinity. We focus on dimension d = 1. We prove that almost surely no such matching has unmatched points. (This question is open for higher d). For each gamma < 1 we establish that there is almost surely a unique such matching, and that it can be expressed as a finitary factor of the points. Moreover, its typical edge length has finite rth moment if and only if r < 1 /2. In contrast, for gamma = 1 there are uncountably many matchings, while for gamma > 1 there are countably many, but it is impossible to choose one in a translation-invariant way. We obtain existence results in higher dimensions (covering many but not all cases). We address analogous questions for one-colour matchings also.
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2.
  • Janson, Svante, et al. (författare)
  • Addendum to The Minimal Spanning Tree in a Complete Graph and a Functional Limit Theorem for Trees in a Random Graph
  • 2006
  • Ingår i: Random structures & algorithms (Print). - : Wiley. - 1042-9832 .- 1098-2418. ; 28:4, s. 511-512
  • Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
    • The minimal weight of a spanning tree in a complete graph Kn with independent, uniformly distributed random weights on the edges is shown to have an asymptotic normal distribution. The proof uses a functional limit extension of results by Barbour and Pittel on the distribution of the number of tree components of given sizes in a random graph.
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