The talk is scheduled in virtual setting, using Zoom platform. The talk will also be live-streamed via YouTube. During the meeting, the questions can be posed via chat or audio for participants in the meeting. Everybody interested is invited to participate in the Zoom meeting, with the limit of 100 participants, or to follow the live-broadcast.
Link to Zoom meeting will be put here few days before the talk:
https://us02web.zoom.us/j/89253380963
Meeting ID: 892 5338 0963
Link to YouTube live broadcast will be put here 10 minutes before the talk.
http://www.youtube.com/watch?v=73pwmKkdKyY
The talk will be in English.
Abstract:
In this talk we will study a Fleming-Viot-type model of particle movement. In the model several particles move around in a domain $D$, independently, until one of them reaches the boundary of the domain. At that moment, the particle on the boundary dies and one of the remaining particles in the domain branches (splits) into two.
This model has been well studied in the discrete setting, i.e. where the movement of the particle is restricted to the to a finite or countable set of points in the domain. However, very little is known in the case when the particle can move to any point in $D$ subset od $R^d$.
We will talk about a specific setting, where the movement of the particle is Brownian motion. We are interested in the long term behavior of this process: How often will the particles branch? Will they be close to the boundary at that point? …
For our analysis we will be using the iterated stochastic sequence $X_n=A_nX_{n-1}+B_n$, where $X_0=0$ and $(A_n,B_n)$ is an i.i.d. sequence of random variables. Although these types of sequences are well known and investigated, the specific case that we will need has not been explored.
Long term behavior of the sequence will be a solution to the stochastic fixed point equation. New and known results will provide a version of Law of the Iterated Logarithm for the Fleming-Viot process.
Based on joint papers and ongoing work with Krzysztof Burdzy (University of Washington, Seattle) and Bartosz Kolodziejek (Warsaw University of Technology).
