Oxford Events, the new replacement for OxTalks, will launch on 16th March. The two-week OxTalks freeze period starts on Monday 2nd March. During this time, there will be no facility to publish or edit events. The existing OxTalks site will remain available to view during this period. Once Oxford Events launches, you will need a Halo login to submit events. Full details are available on the Staff Gateway.
The random walk on the permutations of [N] generated by the transpositions was shown by Diaconis and Shahshahani to mix with sharp cutoff around N log N /2 steps. However, Schramm showed that the distribution of the sizes of the largest cycles concentrates (after rescaling) on the Poisson-Dirichlet distribution PD(0,1) considerably earlier, after (1+\epsilon)N/2 steps. We show that this behaviour in fact emerges precisely during the critical window of (1+\lambda N^{-1/3}) N/2 steps, as \lambda \rightarrow\infty. Our methods are rather different, and involve an analogy with the classical Erdos-Renyi random graph process, the metric scaling limits of a uniformly-chosen connected graph with a fixed finite number of surplus edges, and analysing the directed cycle structure of large 3-regular graphs. Joint work with Christina Goldschmidt.
