Reitzner, Matthias

Prof. Dr. techn. Matthias Reitzner

Lehrveranstaltungen

• Lebensversicherungsmathematik
• Wahrscheinlichkeitstheorie
• Seminar Mathematik des Internets
• Doktorandenseminar Kombinatorische Strukturen in der Geometrie
• Lektüre math. Arbeiten
• Oberseminar Stochastik
• Studienvorkurs Mathematik

• 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

• Extreme points and convex hull of random samples:
  Given a random sample consisting of n iid. realizations of a random variable in Rd. Extreme points of this sample are those points which are on the boundary of the convex hull of the sample. Compute the distribution of the number of extreme points of this sample (which is in general something between d+1 and n).

• Poisson-Voronoi tesselations: Given a Poisson point process, associate to each point the corresponding Voronoi cell (that part of Rd closer to this point than to any other point of the point process). What is the probability of large Voronoi cells (large 'gaps' in the point process)? What is the shape of large Voronoi cells?

• Characterization of valuations: Valuations are additive functionals on certain classes of sets. In particular, they fulfill the inclusion-exclusion property and thus all measures are valuations. Characterize valuations having natural invariance properties.

• 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”

• Poisson-Voronoi Approximation and Wiener-Ito Chaos Expansions. Stochastic Analysis Seminar, Univ. Oxford, February 2011

  
  

• Poisson-Voronoi Approximation. Fields Institute, Toronto, September 2010
  
  

• Affine invariant notions of surface area I -- III. Oberwolfach, Jänner 2010
  
  

• Kann denn Zufall optimal sein? Antrittsvorlesung, Univ. Osnabrück, November 2009

• 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 Comput. Geom., to appear (Gem. mit I. Barany, J.-F. Marckert)
  
  

• Central limit theorems for U-statistics of Poisson point processes.
  Ann. Prob. (2012), to appear (Gem. mit M. Schulte)
  
  

• 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. B'ar'any)
  
  

• 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. B'ar'any)
  
  

• Random polytopes (survey).
  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)