Münchner Mathematische KalenderKalender mit mathematischen Vorträgen im Raum MünchenThu, 13 Sep 2018 09:13:38 +0200
http://mathcal.ma.tum.de/mc/showtalks?
17.09.2018 16:30 Anne-Marie Mößnang (LMU, MSc presentation) : Sharp phase transition for confetti percolation
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1272
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1272Recently, Duminil-Copin, Raoufi and Tassion developed a new method to prove sharp phase transition for Voronoi percolation even in higher dimensions. The idea is based on two main steps: For $S_n(0) := \{x \in \mathbb{R}^d : ||x|| = n\}$ and $\theta_n(p) := P_p(0 \leftrightarrow S_n(0))$, they first prove a family of differential inequalities regarding $\theta_n(p)$. Here, they make use of a randomized algorithm, which determines the function $f := 1_{0 \leftrightarrow S_n(0)}$, and of the OSSS inequality, to estimate the variance of $f$. Second they employ a Lemma to $\theta_n(p)$, which verifies the sharp phase transition. In the talk we transfer this method to prove sharp phase transition for confetti percolation in $\mathbb{R}^d \times (- \infty, 0]$.
17.09.2018 17:15 Florian Rudiger (LMU, MSc presentation) : Recurrence and transience of random geometric graphs
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1273
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1273In this talk, we prove for various graphs that the random walk is recurrent or transient. While in one case the random walk almost surely visits every vertex of the graph infinitely many times, in the other case it eventually escapes any finite set of vertices and never returns. Under certain assumptions on the underlying point process, we apply results from Gurel-Gurevich, Nachmias and Rousselle to get recurrence results for graphs in the plane and transience results for higher dimensions. Apart from that we will mention some classes of point processes for which our results hold.
27.09.2018 15:00 Rangel Baldasso (Bar Ilan University) : TBA
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1282
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1282TBA