OxTalks is Changing
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
Branching Brownian motion with absorption: the slightly subcritical case
Consider branching Brownian motion with absorption in which particles move independently as one-dimensional Brownian motions with drift $-\rho$, each particle splits into two particles at rate one, and particles are killed when they reach the origin. Kesten showed that this process dies out with probability one if and only if $\rho \geq \sqrt{2}$. In this talk I will focus on the subcritical case when $\rho > \sqrt{2}$ and consider two questions:
Firstly, can we obtain Yaglom type results? That is if we condition the process to be alive at large time $t$ what do we see? And if there is some sort of limit distribution, how does it behave when $\rho \searrow \sqrt 2$?
Second, we will study a question related to the so-called consistent maximal displacement: what is the inital position that a partcile must start from so that the process can survive until a large time $t$? We find that there is a phase transition, with the behavior changing when $t$ is of the order $\eps^{-3/2}$.
This is based on joint works with Jiaqi Liu, Bastien Mallein, and Jason Schweinsberg.
Date:
2 June 2025, 14:00
Venue:
Mathematical Institute, Woodstock Road OX2 6GG
Venue Details:
L4
Speaker:
Julien Berestycki (University of Oxford)
Organising department:
Department of Statistics
Part of:
Probability seminar
Booking required?:
Not required
Audience:
Members of the University only
Editors:
Christina Goldschmidt,
Julien Berestycki
