### 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

#### Abstract

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.

#### Video

**The video for this talk should appear here if JavaScript is enabled.**

If it doesn't, something may have gone wrong with our embedded player.

We'll get it fixed as soon as possible.

## Comments

Start the discussion!