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Publication - Dr Mark Hagen

    Global Structural Properties of Random Graphs


    Behrstock, J, Falgas-Ravry, V, Hagen, MF & Susse, T, 2018, ‘Global Structural Properties of Random Graphs’. International Mathematics Research Notices, vol 2018., pp. 1411?1441


    We study two global structural properties of a graph $\Gamma$, denoted AS and CFS, which arise in a natural way from geometric group theory. We study these properties in the Erd\"os--R\'enyi random graph model G(n,p), proving a sharp threshold for a random graph to have the AS property asymptotically almost surely, and giving fairly tight bounds for the corresponding threshold for CFS. As an application of our results, we show that for any constant p and any $\Gamma\in G(n,p)$, the right-angled Coxeter group $W_\Gamma$ asymptotically almost surely has quadratic divergence and thickness of order 1, generalizing and strengthening a result of Behrstock--Hagen--Sisto.

    Full details in the University publications repository