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.