## Oliver Riordan

I am member of the
Mathematical Institute in
the University of Oxford, and
a Tutorial Fellow in Mathematics at St Edmund Hall.

## Research

Most of my research in is probabilistic combinatorics, concentrating on random
graphs and on percolation;
I was a student of Béla Bollobás with whom I still collaborate
frequently. The original purpose of this page was to provide access to some of our papers, which can take a while to appear in mathematics journals. Nowadays, however,
almost all my recent work is available via arXiv.
For a complete (at some point in time) list of publications, see my
list of publications, or
search arXiv.org.

Recently my research student Lutz Warnke and I published a paper in Science about Achlioptas processes:
abstract
reprint
full text

Selected papers on percolation:

The critical probability for random Voronoi percolation in the plane is 1/2, with B. Bollobás,
*Probability Theory and Related Fields* **136** (2006), 417-468.
(arXiv version)

Using methods developed in the above paper, we have written out a short proof of the well-known
result that the critical probability for bond percolation in the square lattice
is 1/2:

A short proof of the Harris-Kesten Theorem, with B. Bollobás,
*Bulletin of the London Mathematical Society* **38** (2006), 470-484.
(arXiv version)

I have also written many papers on inhomogeneous random graphs, mostly with B. Bollobás.
These concern rigorous mathematical analysis of various models motivated by the study
of large scale real-world networks, in particular, `scale-free' and `web-graph' models.
One particular example is our paper with Svante Janson:

The phase transition in inhomogeneous random graphs,
*Random Structures and Algorithms* **31** (2007), 3-122.
(arXiv version)

## Other stuff

Alex Selby and I solved the Eternity puzzle in May 2000; see
Alex's Eternity page.
I'm afraid I can't offer any tips for solving
Eternity II! (It's now too late anyway.)

Last updated 18th April 2012.