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 (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.
