Wintersemester 2026/2027

Stochastische Geometrie und räumliche Statistik

Vorträge:

_{20.10.     Prof. Dr. Peter Grabner – TU Graz - Österreich}

 

Title: Hyperuniformity on Compact Spaces and Quasi-Monte Carlo Aspects  
  

Abstract: Hyperuniformity has been originally introduced and studied as a property of infinite subsets of Euclidean space to describe behaviour intermediate between order and random disorder. For short, one could state this as „better than random“, and this is the point, where hyperuniformity meets with Quasi-Monte Carlo. In both contexts point sets are constructed and analysed, which exhibit quasi-random behaviour, but beat random point sets with respect to some quality measure.

 

Dienstag, 20. Oktober 2026, 16:00 Uhr, Helmholtzstr. 18, Raum 220

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_{27.10      tba.}
 

Title: tba.

Abstract: tba.
 

_{Dienstag, 27. Oktober 2025, 16:00 Uhr, Helmholtzstr. 18, Raum 220}

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_{03.11.    Dr. Tara Trauthwein – Universität Münster}

  

Title: Localization on Poisson point processes
 
Abstract: Consider a Poisson point process on a metric space and a function thereof which consist of a sum of ‘local’ components. Examples of such functions can be the total edge-length or the number of isolated points in a spatial random graph, but they can also include statistics of more complex models like the birth-growth model, which is an interacting particle system. It is known that when those functions exhibit a certain kind of ‘local’ behaviour, then they satisfy a Central Limit Theorem when the underlying point process grows. 

This talk is based on a joint work with Joseph Yukich, where we propose the notion of ‘localization’, a weak condition on score functions which is sufficient to induce a CLT. We give Berry-Esseen type quantitative convergence rates and illustrate our results on several applications, among them the birth-growth model. The proof is based on new and improved second-order Poincaré inequalities for general functions of Poisson point processes, which are of independent interest.

 

_{Dienstag, 03. November 2026, 16:00 Uhr, Helmholtzstr. 18, Raum 220}

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_{10.11.    tba.}

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_{17.11.    tba.}

 

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_{24.11.    Prof. Dr. Daniela Flimmel - Charles University, Prague, Czech Republic}

Title: Tba.

Abstract: Tba.

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2027

_{12.01.    tba.} 

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_{19.01.    tba.} 

_{26.01.    tba.} 

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_{09.02.    tba.} 

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_Gäste:

• Prof. Dr. Peter Grabner – TU Graz - Österreich

• Dr. Tara Trauthwein – Universität Münster

• Prof. Dr. Daniela Flimmel - Charles University, Prague, Czech Republic