FB 6 Mathematik/Informatik

Institut für Mathematik

Navigation und Suche der Universität Osnabrück



Short CV

  • 1990: Master degree (Dipl.-Ing.), Vienna University of Technology
  • 1993: Doctor of Technical Sciences, Vienna University of Technology
  • 1993 - 1999: Vertragsassistent, Vienna University of Technology
  • 1996: Actuary, full member of the Aktuarvereinigung Österreich
  • 1999 - 2001: Assistant Professor, Vienna University of Technology
  • 2001: Habilitation, Vienna University of Technology
  • 2001 - 2009: Associate Professor, Vienna University of Technology
  • 2001 - 2003: Visiting Scholar, University of Freiburg
  • 2003 - 2007: Guest lecturer for Actuarial Mathematics at Universität Salzburg
  • since 2009: Professor of Mathematics, University of Osnabrück
  • since 2011: Director of the Institute of Mathematics
  • since 2013: Spokesman DFG-Graduiertenkolleg Combinatorial Structures in Geometry
  • since 2016: DAV-Correspondent at the University of Osnabrück

Research Interests

I am interested in problems on the borderline between stochastic and geometry:

  • convex geometry
  • geometric valuation theory
  • stochastic geometry and geometric probabilites
  • random convex hulls and extreme points
  • random mosaics and tessellations
  • random CW-complexes
  • random graphs


  • 2013 - 2018: DFG Graduiertenkolleg “Combinatorial Structures in Geometry”
  • 2008 - 2010: FWF Project “Combinatorial Properties of Random Mosaics”
  • 2007 - 2008: Scientist in charge of the Austrian node of "Phenomena in High Dimensions"
  • 2005 - 2007: FWF Project "Valuations on convex bodies" (jointly with Monika Ludwig)

  • 2001 - 2003: FWF Project “The geometric structure of random polytopes”

Recent Talks

  • Stars of Empty Simplices. Oberwolfach, December 2018
  • Concentration of Poisson U-Statistics: Subgraph Counts in Random Geometric Graphs. BIRS, Banff, March 2018
  • Monotonicity of Random Polytopes. Convex and Integral Geometry 2017, Frankfurt, September 2017
  • Random Points on a Halfsphere. AMS sectional meeting, Univ. Athens, USA, März 2016
  • Voronoi trifft Poisson: Zufällige Approximation von Mengen, Weihnachtskolloquium, Universität Bochum, Dezember 2013
  • Large deviation inequality for the Gilbert Graph, Oberwolfach, Februar 2013


Asymptotic normality for random simplices and convex bodies in high dimensions. Submitted (Gem. mit D. Alonso-Gutiérrez, F. Besau, J. Grote, Z. Kabluchko, C. Thäle, B. Vritsiou, E. Werner)

Stars of Empty Simplices. Submitted (Gem. mit D. Temesvari)

Crossing Numbers and Stress of Random Graphs. In: Biedl. T. and Kerren, A. (eds.): Graph Drawing and Network Visualization. LNCS 11282, p. 255-268 (2018). Springer, Cham (Gem. mit M. Chimani, H. Döring)

Facets of high-dimensional Gaussian polytopes. Submitted (Gem. mit K. Böröczky, G. Lugosi)

Gigantic random simplicial complexes. Homology Homotopy Appl., to appear, (Gem. mit J. Grygierek, M. Juhnke-Kubitzke, T. Römer, O. Röndigs)

Production Shock Distribution and Risk Aversion in Multi-Agent-Tournaments. Submitted (Gem. mit B. Hartig)

On the cells in a stationary Poisson hyperplane mosaic. Adv. Geom. 19, 145-150 (2019), (Gem. mit R. Schneider)

Concentration for Poisson U-Statistics: Subgraph Counts in Random Geometric Graphs. Stochastic Process. Appl., 128, 3327-3352 (2018), (Gem. mit S. Bachmann)

Cells with many facets in a Poisson hyperplane tessellation. Adv. Math. 324, 203-240 (2018) (Gem. mit G. Bonnet, P. Calka)

Random Approximation of Convex Bodies: Monotonicity of the Volumes of Random Tetrahedra.Discrete Comput. Geom. 59, 165-174 (2018) (Gem. mit S. Kunis und B. Reichenwallner)

Monotonicity of functionals of random polytopes. In: Ambrus, G., Böröczky, K., and Füredi, Z. (eds.): Discrete Geometry and Convexity. p. 23-28 (2017). A. Renyi Institute of Mathematics, Hungarian Academy of Sciences, Hungary (Gem. mit M. Beermann)

Expected Sizes of Poisson-Delaunay Mosaics and Their Discrete Morse Functions. Adv. Appl. Probab. 49, 745-767 (2017) (Gem. mit H. Edelsbrunner, A. Nikitenko)

SL(n) invariant valuations on polytopes. Discrete Comput. Geom. 57, 571-581 (2017) (Gem. mit M. Ludwig)

Random points in halfspheres. Random Structures & Algor. 50, 3-22 (2017),  (Gem. mit I. B\'ar\'any, D. Hug, und R. Schneider)

Limit theory for the Gilbert graph. Adv. Appl. Math. 88, 26-61 (2017) (Gem. mit M. Schulte und C. Thäle)

Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry. Editors: Peccati, G., Reitzner, M., Bocconi & Springer Series 7; Bocconi University Press, Springer, Milan (2016)

Introduction to Stochastic Geometry. In: Peccati, G. and Reitzner, M. (eds.): Stochastic Analysis for Poisson Point Processes. p. 145-184 (2016). Bocconi & Springer Series 7; Bocconi University Press, Springer, Milan (Gem. mit D. Hug

U-statistics in stochastic geometry. In: Peccati, G. and Reitzner, M. (eds.): Stochastic Analysis for Poisson Point Processes. p. 229-253 (2016). Bocconi & Springer Series 7; Bocconi University Press, Springer, Milan (Gem. mit R. Lachieze-Rey)

On the monotonicity of the moments of volumes of random simplices. Mathematika 62, 949–958 (2016) (Gem. mit B. Reichenwallner)

Beyond the Efron-Buchta identities: distributional results for Poisson polytopes. Discrete Comput. Geom.  53, 226-244 (2015),  (Gem. mit M. Beermann)

Poisson polyhedra in high dimensions. Adv. Math. 281, 1-39 (2015) (Gem. mit J. Hörrmann, D. Hug und C. Thäle)

Poisson point processes: Large deviation inequalities for the convex distance. Electron. Commun. Probab. 18, No. 96, 1-7 (2013)

Central limit theorems for U-statistics of Poisson point processes. Ann. Prob. 41, No. 6, 3879-3909 (2013), (Gem. mit M. Schulte).

The monotonicity of f-vectors of random polytopes. Electron. Commun. Probab. 18, No. 23, 1-8 (2013) (Gem. mit O. Devillers, M. Glisse , X. Goaoc, G. Moroz)

Many empty triangles have a common edge. Discrete Comp. Geom. 50, 244-252 (2013), (Gem. mit I. Barany, J.-F. Marckert).

Set Reconstruction by Voronoi cells. Adv. Appl. Probab. 44, 938-953 (2012) (Gem. mit E. Spodarev, D. Zaporozhets).

On the variance of random polytopes. Adv. Math. 225, 1986-2001 (2010) (Gem. mit I. Barany).

A classification of SL(n) invariant valuations. Ann. of Math. (2) 172, 1219-1267 (2010) (Gem. mit M. Ludwig).

Poisson Polytopes. Ann. Prob. 38, 1507-1531 (2010) (Gem. mit I. Barany).

Random polytopes. In: Molchanov, I. and Kendall, W. (eds.): New perspectives in stochastic geometry. p. 45-76 (2010). Oxford University Press, Oxford.

Mean width of inscribed random polytopes in a reasonable smooth convex body. J. Multivariate Anal. 100, 2287-2295 (2009), (Gem. mit K. Böröczky jr., F. Fodor, V. Vigh).

Poisson-Voronoi Approximation. Ann. Appl. Probab. 19, 719-736 (2009), (Gem. mit M. Heveling).

Elementary moves on triangulations. Discrete Comput. Geom. 35, 527-536 (2006) (Gem. mit M.Ludwig).

Central limit theorems for random polytopes. Probab. Theory Relat. Fields 133, 483-507 (2005). (Thanks to J. Pardon who pointed out an error in my proof, see Central limit theorems for uniform model random polygons, p.6).

The combinatorial structure of random polytopes. Adv. Math. 191, 178-208 (2005).

Gaussian polytopes: variances and limit theorems. Adv. Appl. Probab. 37, 297-320 (2005) (Gem. mit D.Hug).

The limit shape of the zero cell in a stationary Poisson hyperplane tesselation. Ann. Prob. 32, 1140-1167 (2004), (Gem. mit D. Hug und R. Schneider).

Asymptotic mean values of Gaussian polytopes. Beitr. Algebra Geom. 45, 531-548 (2004), (Gem. mit D.Hug und G.O. Munsonius).

Electromagnetic wave propagation and inequalities for moments of chord lengths. Adv. Appl. Probab. 36, 987-995 (2004), (Gem. mit J. Hansen).

Large Poisson-Voronoi cells and Crofton cells. Adv. Appl. Probab. 36, 667-690 (2004), (Gem. mit D. Hug und R. Schneider).

Efficient indoor radio channel modeling based on Integral Geometry. IEEE Transactions on Antennas and Propagation 52, 2456-2463 (2004), (Gem. mit J. Hansen).

Approximation of smooth convex bodies by random circumscribed polytopes. Ann. Appl. Probab. 14, 239-273 (2004) (Gem. mit K. Böröczky)

Stochastical approximation of smooth convex bodies. Mathematika 51, 11-29 (2004).

Random polytopes and the Efron-Stein jackknife inequality. Ann. Prob. 31, 2136-2166 (2003).

Random polytopes are nearly best-approximating. Rend. Circ. Mat. Palermo Suppl. 70, 263-278 (2002).

Random points on the boundary of smooth convex bodies. Trans. Amer. Math. Soc. 354, 2243-2278 (2002).

The floating body and the equiaffine inner parallel curves of a convex body. Geom. Dedicata 84, 151-167 (2001).

The convex hull of random points in a tetrahedron: Solution of Blaschke's problem and more general results. J. Reine Angew. Math. 536, 1-29 (2001) (Gem. mit C. Buchta).

Inequalities for convex hulls of random points. Monatsh. Math. 131, 71-78 (2000).

On Gram-Charlier expansion in risk theory. Working Paper of the Lab. of Act. Math., Univ. Copenhagen 161, 1-30 (1999) (Gem. mit C. Buchta).

A characterization of affine surface area. Adv. Math. 147, 138-172 (1999) (Gem. mit M. Ludwig).

On a theorem of G. Herglotz about random polygons. Rend. Circ. Mat. Palermo Suppl. 50, 89-102 (1997) (Gem. mit C. Buchta).

Equiaffine inner parallel curves of a plane convex body and the convex hulls of randomly chosen points. Probab. Theory Relat. Fields 108, 385-415 (1997) (Gem. mit C. Buchta).

Optimaler Selbstbehalt in der Kraftfahrzeug-Haftpflichtversicherung. Nicht zur Veröffentlichung bestimmter Forschungsbericht, Wien, 1995, 59 Seiten (Gem. mit C. Buchta).

Zufällige Polytope im Tetraeder. Dissertation, TU-Wien (1993).