"Vergesst die Zeit. Ich will euch Geschichten erzählen." : Der Kinderbuchforscher Klaus Doderer veröffentlicht Biografie von James Krüss

Rezension zu: Klaus Doderer : James Krüss – Insulaner und Weltbürger Hamburg 2009, Carlsen Verlag, 363 Seiten, ISBN 978-3-551-58213-3, 19,90 Euro

Upper large deviations for power-weighted edge lengths in spatial random networks

We study the large-volume asymptotics of the sum of power-weighted edge lengths $\sum_{e \in E}|e|^\alpha$ in Poisson-based spatial random networks. In the regime $\alpha > d$, we provide a set of sufficient conditions under which the upper large deviations asymptotics are characterized by a condensation phenomena, meaning that the excess is caused by a negligible portion of Poisson points. Moreover, the rate function can be expressed through a concrete optimization problem. This framework encompasses in particular directed, bidirected and undirected variants of the $k$-nearest neighbor graph, as well as suitable $\beta$-skeletons.Comment: 27 pages, 5 figure