## Pete's website

A little bit about everything Pete related

Welcome to my personal site. Here, you can find my research interests, as well as past and current work. There is also an informal CV to be found somewhere below. Finally, ways to reach and/or find me are located on the right (if visiting from a mobile device, use the menu button in the upper right corner. Hope you enjoy your stay!

### Seminar: Percolation (Summer Semester 2019)

In this seminar we will take a closer look at an area of probability that originates in a very applied problem, but leads to many interesting theoretical questions. Suppose we submerge a large porous rock into water. Can the water reach its center? In other words, how does a fluid ﬂow in a porous medium where the different channels and paths are randomly blocked? Mathematically speaking, we are interested in the component structure of random subgraphs of graphs.

We will start by looking at the case where the underlying graph is the square lattice \(\mathbb{Z}^2\) and the subgraph is obtained by removing edges independently with some probability \(p > 0\). We will answer questions such as how the choice of \(p\) influences the probability that a fluid percolates across the entire graph and how this behavior changes drastically at some specific value of \(p\). Towards the end of the seminar we will take a closer lo ok at newer results such as conformal invariance and Smirnov’s Theorem.

### Publications

#### Submitted papers

**The age-dependent random connection model**

with Arne Grauer, Lukas Lüchtrath and Peter Mörters

#### Published papers

**Percolation of Lipschitz surface and tight bounds on the spread of information among mobile agents**

with Alexandre Stauffer,*APPROX-RANDOM 2018*: 39:1-39:17**Multi-scale Lipschitz percolation of increasing events for Poisson random walks**

with Alexandre Stauffer,*Annals of Applied Probability*, 29 (2019), 376-433**Random walks in random conductances: decoupling and spread of infection**

with Alexandre Stauffer,*Stochastic Processes and their Applications*, to appear

### Mini CV

Since this is supposed to be a sort of CV website, I should probably list a couple of things that define me. In no specific order, here's a few things I have done.