A coupled model for the indegree and outdegree analysis of the web

We introduce a mixed model for web graph which simul- taneously describes the inlink and outlink distributions, by taking into account the interconnection of the two processes. We derive the expression for the steady-state distribution of indegrees (outdegrees) among vertices with fixed outde- gree (indegree) in terms of sums of Beta functions. The experimentation on subsets of the real web shows that the proposed distributions well reproduce the behaviour of the observed data

THE COLLISION SPECTRUM OF Lambda-COALESCENTS

$\Lambda$-coalescents model the evolution of a coalescing system in which any number of blocks randomly sampled from the whole may merge into a larger block. For the coalescent restricted to initially $n$ singletons we study the collision spectrum $(X_{n,k}:2\le k\le n)$, where $X_{n,k}$ counts, throughout the history of the process, the number of collisions involving exactly $k$ blocks. Our focus is on the large $n$ asymptotics of the joint distribution of the $X_{n,k}$'s, as well as on functional limits for the bulk of the spectrum for simple coalescents. Similarly to the previous studies of the total number of collisions, the asymptotics of the collision spectrum largely depends on the behaviour of the measure $\Lambda$ in the vicinity of $0$. In particular, for beta$(a,b)$-coalescents different types of limit distributions occur depending on whether $02$.Comment: 21 pages, submitte