Christian Hirsch

Christian Hirsch

Associate Professor for Data Science and Statistics

Aarhus University

Christian Hirsch

I am Associate Professor for Data Science and Statistics at Aarhus University, where I am studying random networks motivated from biology and health sciences via techniques from topological data analysis and stochastic geometry. I am a member of the Stochastics group at the Department of Mathematics. I am also affiliated with the AU DIGIT Centre.

Before that, I was Assistant Professor at the University of Groningen and 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

  • Statistical foundations of topological data analysis
  • Large deviations theory in stochastic geometry
  • Percolation theory of spatial random networks

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.

Large deviations

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.

Spatial random 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.

Research

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Upper large deviations for power-weighted edge lengths in spatial random networks

We study the large-volume asymptotics of the sum of power-weighted edge lengths in Poisson-based spatial random networks. In the regime …
C. Hirsch, D. Willhalm
PDF Project
Upper large deviations for power-weighted edge lengths in spatial random networks

On the consistency and asymptotic normality of multiparameter persistent Betti numbers

The persistent Betti numbers are used in topological data analysis to infer the scales at which topological features appear and …
M. B. Botnan, C. Hirsch
PDF Project
On the consistency and asymptotic normality of multiparameter persistent Betti numbers

Connection intervals in multi-scale dynamic networks

We consider a hybrid spatial communication system in which mobile nodes can connect to static sinks in a bounded number of intermediate …
C. Hirsch, B. Jahnel, E. Cali
PDF Project
Connection intervals in multi-scale dynamic networks

Infinite WARM graphs III, strong reinforcement regime

We study the random subgraph $\mathcal E$, consisting of edges reinforced infinitely often, in a reinforcement model on infinite …
C. Hirsch, M. Holmes, V. Kleptsyn
PDF
Infinite WARM graphs III, strong reinforcement regime

Asymptotic properties of one-layer artificial neural networks with sparse connectivity

A law of large numbers for the empirical distribution of parameters of a one-layer artificial neural networks with sparse connectivity …
C. Hirsch, M. Neumann, V. Schmidt
PDF Project
Asymptotic properties of one-layer artificial neural networks with sparse connectivity
See all publications

Teaching

Supervision

  • Postdocs
  • PhD theses
    • N.N. Lundbye (since 02/23). Statistical foundations of TDA
    • P. Juhasz (since 11/22). TDA-based models of evolving higher-order networks
    • D. Willhalm (since 05/20). Large deviations in stochastic geometry
  • MSc theses
    • L. de Jonge (07/21). Absence of WARM percolation on geometric networks
    • Y. Couzinié (09/18). Sublinearly reinforced Pólya urns on graphs of bounded degree
    • F. Rudiger (09/18). Recurrence and transience of graphs generated by point processes
    • A. Hinojosa Calleja (08/16). Interference in ad-hoc telecommunication systems in the high-density limit
    • E. Rolly (06/16). Gibbs-Masse für Trajektorien von Nachrichten in einem Kommunikationsnetzwerk
    • A. Tóbiás (04/16). Highly dense mobile communication networks with random fadings
  • BSc theses
    • H. Hansen (??/24). Convex hull algorithms for the triangulation/construction of alpha complexes
    • B. Hautorp (06/23). Asymptotic normality of tessellation-based persistent Betti numbers
    • B. Buttenschøn (06/23). A law of large numbers for wide one-layer neural networks
    • L. Kriouar (07/21). Analysis of financial data with time series and persistent homology
    • H. Hong (07/21). Geometric and topological approaches to mode clustering
    • J. Langenbahn (12/19). Konvergenz des Pseudo-Marginalen MCMC Verfahren
    • H. Blocher (02/18). Poisson Matching
    • F. Brück (06/17). Percolation properties of Poisson graphs

Contact