##### Department of Mathematics,

University of California San Diego

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### Math 286 - Stochastic Systems Seminar

## Massimo Franceschetti

#### Electrical and Computer Engineering, UCSD

## Random networks for communications

##### Abstract:

The theory of random graphs is a useful mathematical tool to describe many real world systems. Recently, the mathematical and engineering communities have shown a renewed interest in the geometric version of these models. The nodes are geometrically distributed at random, and pairs of nodes are connected by edges, whose presence depends on the random positions of the nodes in the plane. One emerging application is in the field of wireless communications, where radio transmitting stations communicate by radiating electromagnetic waves. In this talk, first I review several models of random networks for communication that are directly related to continuum percolation. Then, I show some recent results on connectivity of dependent percolation models of interference limited networks. Finally, I introduce the Gupta-Kumar concept of throughput scaling, and argue how this can be obtained as a natural consequence of the RSW theorem in percolation theory.

Host: Ruth Williams

### May 10, 2006

### 4:00 PM

### AP&M 7218

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