Non-central limit theorems in geometric probability

Consider a graph with n vertices placed randomly in the unit

square, each connected by an edge to its nearest neighbour in a

south-westerly direction. For many graphs of this type, the centred

total length is asymptotically normal for n large, but in the

present case the limit distribution is not normal, being defined in

terms of fixed-point distributions of a type seen more commonly in

the analysis of algorithms. We discuss related results. This is

joint work with Andrew Wade.