caa a22 4500 445391898 CHVBK 20180317143049.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10955-011-0122-1 doi (NATIONALLICENCE)springer-10.1007/s10955-011-0122-1 Strict Inequalities of Critical Values in Continuum Percolation [Elektronische Daten] [Massimo Franceschetti, Mathew Penrose, Tom Rosoman] We consider the supercritical finite-range random connection model where the points x,y of a homogeneous planar Poisson process are connected with probability f(|y−x|) for a given f. Performing percolation on the resulting graph, we show that the critical probabilities for site and bond percolation satisfy the strict inequality $p_{c}^{\mathrm{site}} > p_{c}^{\mathrm{bond}}$. We also show that reducing the connection function f strictly increases the critical Poisson intensity. Finally, we deduce that performing a spreading transformation on f (thereby allowing connections over greater distances but with lower probabilities, leaving average degrees unchanged) strictly reduces the critical Poisson intensity. This is of practical relevance, indicating that in many real networks it is in principle possible to exploit the presence of spread-out, long range connections, to achieve connectivity at a strictly lower density value. The Author(s), 2011 Bond percolation nationallicence Site percolation nationallicence Gilbert graph nationallicence Random connection model nationallicence Franceschetti Massimo Department of Electrical and Computer Engineering, University of California San Diego, 9500 Gilman Drive, Mail Code 0407, 92093-0407, La Jolla, CA, USA aut Penrose Mathew Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK aut Rosoman Tom Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/3(2011-02-01), 460-486 0022-4715 142:3<460 2011 142 10955 https://doi.org/10.1007/s10955-011-0122-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0122-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Franceschetti Massimo Department of Electrical and Computer Engineering, University of California San Diego, 9500 Gilman Drive, Mail Code 0407, 92093-0407, La Jolla, CA, USA aut NATIONALLICENCE 700 1- Penrose Mathew Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK aut NATIONALLICENCE 700 1- Rosoman Tom Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/3(2011-02-01), 460-486 0022-4715 142:3<460 2011 142 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer