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Disputation Toyomu Matsuda

12.09.2023 | 10:00
Thema der Dissertation:
Fractional Stochastic Calculus via Stochastic Sewing
Thema der Disputation:
On random interlacements
Abstract: In the seminal work (Ann. of Math, 2010), Sznitman introduced a model of random interlacements that consists of doubly infinite trajectories on $\mathbb{Z}^d$ ($d ≥ 3$), where trajectories are essentially sampled from those of two-sided simple random walk. Random interlacements arise as the limiting distribution of the trace of simple random walk on the torus of size $N$ run by time $u \times N^d$, with some positive parameter $u$. Alternatively, they can be defined through certain Poisson point process on the space of trajectories on $\mathbb{Z}^d$, with the parameter $u$ measuring how many trajectories come into the picture.
In the first part of the talk, a pedagogical overview of random interlacements will be provided.
Especially, we discuss the phase transition of the model with respect to the parameter $u$; that is, for small $u$ the complement of random interlacements possesses a unique unbounded component, while all components are finite for large $u$. In the second part of the talk, we briefly review another innovative work (Invent. Math, 2023) by Sznitman on the asymptotic probability regarding regions disconnected by random interlacements.

Zeit & Ort

12.09.2023 | 10:00

Seminarraum 031
(Fachbereich Mathematik und Informatik, Arnimallee 7, 14195 Berlin)