OxTalks will soon move to the new Halo platform and will become 'Oxford Events.' There will be a need for an OxTalks freeze. This was previously planned for Friday 14th November – a new date will be shared as soon as it is available (full details will be available on the Staff Gateway).
In the meantime, the OxTalks site will remain active and events will continue to be published.
If staff have any questions about the Oxford Events launch, please contact halo@digital.ox.ac.uk
We study the question of whether there exist double points on the boundaries of clusters in Brownian loop-soups — an object introduced by Lawler and Werner in 2004. This question is closely related to our earlier works (with Werner) on the decomposition of Brownian loop-soup clusters. More concretely, we introduce a notion of disconnection exponents which generalizes the Brownian disconnection exponents derived by Lawler, Schramm and Werner in 2001. By computing the generalized disconnection exponents, we can predict the dimension of multiple points on the cluster boundaries in loop-soups. However, for the critical intensity of loop-soup, the dimension of double points on the cluster boundaries appears to be zero, leaving the open problem of whether such points exist for the critical loop-soup.
