Lace expansion and mean-field behavior for the random connection model

  • We study the random connection model driven by a stationary Poisson process. In the first part of the paper, we derive a lace expansion with remainder term in the continuum and bound the coefficients using a new version of the BK inequality. For our main results, we consider three versions of the connection function φ: a finite-variance version (including the Boolean model), a spread-out version, and a long-range version. For sufficiently large dimension (resp., spread-out parameter and d>6), we then prove the convergence of the lace expansion, derive the triangle condition, and establish an infra-red bound. From this, mean-field behavior of the model can be deduced. As an example, we show that the critical exponent γ takes its mean-field value γ=1 and that the percolation function is continuous.

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Author:Markus HeydenreichGND, Remco van der Hofstad, Günter Last, Kilian Matzke
Frontdoor URL
Parent Title (English):arxiv
Year of first Publication:2022
Release Date:2023/04/21
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Latest Publications (not yet published in print):Aktuelle Publikationen (noch nicht gedruckt erschienen)