On 28th November OxTalks will move to the new Halo platform and will become 'Oxford Events' (full details are available on the Staff Gateway).
There will be an OxTalks freeze beginning on Friday 14th November. This means you will need to publish any of your known events to OxTalks by then as there will be no facility to publish or edit events in that fortnight. During the freeze, all events will be migrated to the new Oxford Events site. It will still be possible to view events on OxTalks during this time.
If you have any questions, please contact halo@digital.ox.ac.uk
The (α,β)-superprocess is a spatial branching model associated to an α-stable spatial motion and a (1+β)-stable branching mechanism. Formally, it is a measure-valued Markov process, but this talk concerns the absolutely continuous parameter regime, in which the random measure has a density. After introducing this process and some classical results, I will discuss some newly proven path properties of the density. These include (i) strict positivity of the density at a fixed time (for certain values of α and β) and (ii) a classification of the measures which the density “charges” almost surely, and of the measures which the density fails to charge with positive probability, when conditioned on survival. The duality between the superprocess and a fractional PDE is central to our method, and I will discuss how the probabilistic statements above correspond to new results about solutions to the PDE.
