# Christian Hirsch

I am Assistant Professor for Topological Data Analysis at the University of Groningen. I am affiliated with both the CogniGron and the Probability and Statistics Group, where I am studying random networks motivated from materials science and biology via techniques from topological data analysis and stochastic geometry.

Before that, I was Assistant Professor at the University of Mannheim. I was Postdoc at Aalborg University, at the LMU Munich and the WIAS Berlin. I received my PhD from Ulm University.

### Interests

• limit theorems in topological data analysis
• stochastic channel models
• statistical modeling and analysis of networks in materials science
• random networks in statistical physics
• interplay between dynamical systems and probability

### Education

• PhD in Mathematics, 2014

Ulm University

• Diploma in Mathematics, 2010

LMU Munich

# Projects

### Topological data analysis

Topological data analysis is based on an equally simple as intriguing principle. Leverage invariants from algebraic topology to gain novel insights into data. TDA is now applied in a wide variety of disciplines.

### Inference in channel models

Channel modeling lies at the very foundation of wireless communication and is the basis for simulations of more complex communication systems.

### Random network models for synaptic plasticity

Despite many parallels, there remain fundamental differences how artificial and real neural networks operate. This leads to the question:What properties should a dynamic network have to support the learning of complex patterns?

### Wireless communication networks

In the context of the Internet of Things and in 5G cellular networks, Device-to-Device (D2D) communication plays a key role. This technology aims to reduce the load on the base station by allowing users to communicate with one another, either directly or through several intermediate steps.

### Large deviations in stochastic geometry

What is the probability that a random geometric graph in a sampling window has atypically few or atypically many edges or triangles? What are the sources leading to such rare events? These examples illustrate the core questions of large devations in geometric probability.

# Preprints and Publications

Quickly discover relevant content by filtering publications.

### Maximum likelihood calibration of stochastic multipath radio channel models

We propose Monte Carlo maximum likelihood estimation as a novel approach in the context of calibration and selection of stochastic …

### Extremal life times of persistent loops and holes

Persistent homology captures the appearances and disappearances of topological features such as loops and holes when growing disks …

### Absence of WARM percolation in the very strong reinforcement regime

We study a class of reinforcement models involving a Poisson process on the vertices of certain infinite graphs G. When a …

### Functional central limit theorems for persistent Betti numbers on cylindrical networks

We study functional central limit theorems (FCLTs) for persistent Betti numbers obtained from networks defined on a Poisson point …

### WARM percolation on a regular tree in the strong reinforcement regime

We consider a class of reinforcement processes, called WARMs, on tree graphs. These processes involve a parameter $\alpha$ which …

# Supervision

• PhD theses
• D. Willhalm (since 05/20, University of Groningen). Large deviations in stochastic geometry
• MSc theses
• L. de Jonge (since 10/20, University of Groningen). Percolation in reinforcement-based models for synaptic plasticity
• Y. Couzinié (09/18, LMU Munich). Sublinearly reinforced Pólya urns on graphs of bounded degree
• F. Rudiger (09/18, LMU Munich). Recurrence and transience of graphs generated by point processes
• A. Hinojosa Calleja (08/16, TU Berlin). Interference in ad-hoc telecommunication systems in the high-density limit
• E. Rolly (06/16, TU Berlin). Gibbs-Masse für Trajektorien von Nachrichten in einem Kommunikationsnetzwerk
• A. Tóbiás (04/16, TU Berlin). Highly dense mobile communication networks with random fadings
• BSc theses
• J. Langenbahn (12/19, University of Mannheim): Konvergenz des Pseudo-Marginalen MCMC Verfahren
• H. Blocher (02/18, LMU Munich): Poisson Matching
• F. Brück (06/17, LMU Munich): Percolation properties of Poisson graphs

# Group seminar

### Improved network reconstruction with shrinkage-based Gaussian graphical models

Gaussian graphical models (GGMs) are undirected network models where the nodes represent the random variables and the edges their …

### Stochastic modelling of COVID-19 spread in Italy

Italy was particularly hard hit during COVID-19 pandemic and the aim of this work is to describe the dynamics of infections within each …

### Non Homogeneous Dynamic Bayesian Network Models

One of the main objectives of systems biology is to learn network topologies from gene expression time series. The ultimate goal is to …

### Sharp thresholds for Glauber dynamics percolation

Sharp threshold is a phenomena that characterizes abrupt change of behavior in a phase transition. In this talk, we prove that the …

### A class of stick breaking models

(Joint work with Krishanu Maulik and Subhabrata Sen). We start with a white stick of unit length and for a uniformly chosen point, we …