Tid: 5 december 2011 kl 15.15-16.00.

Föredragshållare: Takis Konstantopoulos, Uppsala universitet.

Titel: Limit theorems for a random directed slab graph

Abstract: We consider a stochastic directed graph on the integers whereby a directed edge between i and a larger integer j exists with probability p_j-i depending solely on the distance between the two integers. Under broad conditions, we identify a regenerative structure that enables us to prove limit theorems for the maximal path length in a long chunk of the graph. We then consider a similar type of graph but on the `slab' ZxI, where I is a finite partially ordered set. We extend the techniques introduced in the in the first part of the paper to obtain a central limit theorem for the longest path. When I is linearly ordered, the limiting distribution can be seen to be that of the largest eigenvalue of a random matrix.

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