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H 1 Weighted distances in scale free random graphs

Auteurs : Komjathy, Julia (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In this talk I will review the recent developments on weighted distances in scale free random graphs as well as highlight key techniques used in the proofs. We consider graph models where the degree distribution follows a power-law such that the empirical variance of the degrees is infinite, such as the configuration model, geometric inhomogeneous random graphs, or scale free percolation. Once the graph is created according to the model definition, we assign i.i.d. positive edge weights to existing edges, and we are interested in the proper scaling and asymptotic distribution of weighted distances.
    In the infinite variance degree regime, a dichotomy can be observed in all these graph models: the edge weight distributions form two classes, explosive vs conservative weight distributions. When a distribution falls into the explosive class, typical distances converge in distribution to proper random variables. While, when a distribution falls into the conservative class, distances tend to infinity with the model size, according to a formula that captures the doubly-logarithmic graph distances as well as the precise behaviour of the distribution of edge-weights around the origin. An integrability condition decides into which class a given distribution falls.
    This is joint work with Adriaans, Baroni, van der Hofstad, and Lodewijks.

    Codes MSC :
    05C80 - Random graphs
    60C05 - Combinatorial probability
    60D05 - Geometric probability and stochastic geometry
    90B15 - Network models, stochastic

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 26/10/2017
      Date de captation : 24/10/2017
      Collection : Research talks
      Format : MP4
      Durée : 00:51:45
      Domaine : Probability & Statistics ; Combinatorics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-10-24_Komjathy.mp4

    Informations sur la rencontre

    Nom du congrès : Dynamics on random graphs and random maps / Dynamiques sur graphes et cartes aléatoires
    Organisteurs Congrès : Ménard, Laurent ; Nolin, Pierre ; Schapira, Bruno ; Singh, Arvind
    Dates : 23/10/2017 - 27/10/2017
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1672.html

    Citation Data

    DOI : 10.24350/CIRM.V.19228803
    Cite this video as: Komjathy, Julia (2017). Weighted distances in scale free random graphs. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19228803
    URI : http://dx.doi.org/10.24350/CIRM.V.19228803

    Voir aussi


    1. Adriaans, E., & Komjathy, J. (2017). Weighted distances in scale-free configuration models. - https://arxiv.org/abs/1709.09481

    2. Baroni, E., van der Hofstad, R., & Komjathy, J. (2016). Tight fluctuations of weight-distances in random graphs with infinite-variance degrees. - https://arxiv.org/abs/1609.07269