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The percolation benefit of spreading random connection functions

Franceschetti, M (San Diego)
Wednesday 07 April 2010, 13:45-14:45

Seminar Room 1, Newton Institute


We consider random connection models in Euclidian space. Although it is in general not possible to determine the exact percolation threshold for the resulting random graphs, we ask a perhaps simpler but related question, namely how the percolation threshold changes with the shape of the connection function. It turns out that for a natural spreading transformation of the connection function, the critical density for these models decreases \emph{strictly} to its limiting value. This indicates that in many real networks it is in principle possible to exploit the presence of spread-out, long range connections to achieve connectivity more easily, at a strictly lower density value. In the course of the talk, we will describe some previous results on spreading transformations and spread-out limits, we will try to emphasize the role of long-range connections for reaching connectivity, and we will mention some open problems. Finally, we will also hint at the role of the strict inequality $p_c^{ bond} < p_c^{site}$ to prove the strict monotonicity result.


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