Yuki Tokushige - Scaling limits of a SRW on the Long-Range percolation cluster (online)
| Dates: | 28 September 2022 |
|---|
| Times: | 15:00 - 16:00 |
|---|
| What is it: | Seminar |
|---|
| Organiser: | Department of Mathematics |
|---|
|
|
Yuki Tokushige (Kyushu University) will speak in the Probability seminar.
In this talk, we will discuss a Long-Range Percolation (LRP) on $\mathbb{Z}^d$, which is a variant of the classical nearest-neighbor Bernoulli percolation. In particular, we consider a problem concerning a SRW on the infinite cluster of a LRP. In the paper published in 2013, Crawford and Sly proved that a SRW on the infinite cluster scales to $\alpha$-stable process. However, they completed the proof only when $\alpha\in(0, 1)$. It is because the remaining case involves a technical problem to do with a control of short jumps of a SRW, which is related to the fact that sample paths of $\alpha$-stable process have infinite variations for $\alpha\in[1, 2)$. In this talk, we will give a brief overview of this subject and explain our idea to overcome the technical issue depicted above and complete the proof of the case $\alpha\in[1, 2)$. This talk is based on a joint work with Noam Berger (Technical University of Munich).
Travel and Contact Information
Find event
https://zoom.us/j/97662591193
