Segnalo il seguente seminario, che si terrà Martedì prossimo in Sapienza.
*Martedì 8 Ottobre, ore 14:00* Sala di Consiglio, Dipartimento di
Matematica, Sapienza Università di Roma
*Speaker:* Dieter Mitsche (Pontificia Universidad Católica de Chile)
*Title: *Component sizes in spatial random graphs
*Abstract:* We consider a large class of spatially-embedded random graphs
that includes among others long-range percolation, continuum scale-free
percolation and the age-dependent random connection model. We assume that
the parameters are such that there is an infinite component. We identify
the stretch-exponent $\zeta$ of the subexponential decay of the
cluster-size distribution. That is, with $|\CC(0)|$ denoting the number of
vertices in the component of the vertex at $0\in \R^d$, we prove $ P (k\le
|\CC(0)|<\infty)=\exp\big(-\Theta(k^{\zeta})\big), $ as $k$ tends to
infinity. The value of $\zeta$ undergoes several phase transitions with
respect to three main model parameters: the Euclidean dimension $d$, the
power-law tail exponent $\tau$ of the degree distribution and a long-range
parameter $\alpha$ governing the presence of long edges in Euclidean space.
Joint work with Joost Jorritsma and Julia Komjáthy.
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Vittoria Silvestri
Assistant Professor
Department of Mathematics
University "La Sapienza"
Piazzale Aldo Moro, 5
00185 - Rome
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