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 and an Associate Fellow of the Aarhus Institute for Advanced Studies. I am also affiliated with the AU DIGIT Centre and the AU Quantum Campus.

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.

TDA summer school; August 04 - August 08, 2025. More details at Topological data analysis in stochastic geometry and image processing.

Interests

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

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

The concepts of percolation and chemical distances concern some of the most fundamental properties of large networks. Loosely speaking, they help to form an intuition what proportion of network nodes are connected and how long it takes of traveling from one node to another. While for simple combinatorial networks, these notions have been studied vigorously, for networks in Euclidean space with complicated spatial correlation patterns, the research is still in its infancy.

Research

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Functional central limit theorem for topological functionals of Gaussian critical points

We study normal approximation of subgraph counts in a model of spatial scale-free random networks known as the age-dependent random …
C. Hirsch, R. Lachièze-Rey, T. Owada
PDF Project
Functional central limit theorem for topological functionals of Gaussian critical points

Large Deviation Analysis for Canonical Gibbs Measures

In this paper, we present a large deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with …
C. Hirsch, M. Petráková
PDF Project
Large Deviation Analysis for Canonical Gibbs Measures

On the topology of higher-order age-dependent random connection models

In this paper, we investigate the potential of the age-dependent random connection model (ADRCM) with the aim of representing …
C. Hirsch, P. Juhász
PDF Project
On the topology of higher-order age-dependent random connection models

Normal approximation for Gibbs processes via disagreement couplings

This work improves the existing central limit theorems (CLTs) on Gibbs processes in three aspects. First, we derive a CLT for weakly …
C. Hirsch, M. Otto, A. M. Svane
PDF Project
Normal approximation for Gibbs processes via disagreement couplings

Large deviations of one-hidden-layer neural networks

In this work, we study large deviation properties of the covariance process in fully connected Gaussian deep neural networks. More …
L. Andreis, F. Bassetti, C. Hirsch
PDF Project
Large deviations of one-hidden-layer neural networks
See all publications

Teaching

Supervision

  • Postdocs
  • PhD theses
  • MSc theses
    • C. Perch (06/25). Monte Carlo Methods and Importance Sampling Techniques for Forecasting Macroeconomic Risks
    • R.H. Nielsen (06/25). Analyzing the Simulation of Semistationary Processes
    • M.H. Petersen-Westergaard (06/25). Efficient Monte Carlo Methods for Estimating Nonlinear Financial Models
    • L. de Jonge (07/21). Absence of WARM percolation on geometric networks. Now, PhD student at the University of Osnabrück.
    • Y. Couzinié (09/18). Sublinearly reinforced Pólya urns on graphs of bounded degree. Now, Postdoc at the Tokyo Institute of Technology.
    • 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. Now, Assistant Professor at Budapest University of Technology.
  • BSc theses
    • O.E. Bech and E.J. Elberg (06/25). Improving Coronary artery segmentation for tachycardia patient
    • J.S. Knudsen and F. Nordberg (06/25). Prediction of coronary artery calcification in breast cancer radiotherapy CT-scan
    • C.D. Fuglkjær and M. Fridorf (06/25). Federated learning with applications in dentistry
    • T. Brejner (06/25). Rare-event simulation for random connection models
    • K.B. Bräuner and A. Kristensen (05/24). Forudgående tidsbestilling for patienter
    • J. Borg (05/24). Markov beslutningsteori: Optimal opladning af elbiler
    • A.P. Diakovasilis and L.V. Jacobsen (05/24). Optimal ambulanceudsendelse
    • M.-C. Mociran (05/24). Optimering af blodplader oplagring
    • F. Tækker (05/24). Screening og behandling af kroniske sygdomme
    • C. Teoridis (05/24). Optimal tildeling af forespørgsler blandt tradløse sensornetværk og databaser
    • C.S. Pallesen (05/24). Forudgående patientkonsultationsplanlægning
    • H.C. Hansen (01/24). Convex hull algorithms for the triangulation/construction of alpha complexes
    • B.H. Kristensen (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
    • F. Brück (06/17). Percolation properties of Poisson graphs
    • 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

Contact