• Lehre

    WS 2018/19 Stochastische Prozesse und Masterseminar zur Wahrscheinlichkeitstheorie
    SS 18 Extremwerttheorie und Punktprozesse und Masterseminar zur Wahrscheinlichkeitstheorie
    WS 2017/18 Wahrscheinlichkeitstheorie II und Masterseminar zur Statistik
    WS 2016/17 Mathematische Statistik und Bachelorseminar zur Wahrscheinlichkeitstheorie
    SS 2016 Wahrscheinlichkeitstheorie und Masterseminar zur Wahrscheinlichkeitstheorie
    WS 2015/16 Stochastik und Masterseminar zu stochastischen Prozessen
    SS 15 Extremwerttheorie und Punktprozesse und Bachelor-Seminar über Markov-Prozesse
    WS 14/15 Mathematische Statistik

    Die Übungsblätter können Sie auf der Homepage der jeweiligen Vorlesung finden. 
    Frühere Lehrveranstaltungen an der Universität Ulm

  • Skripte und Aufgabensammlungen

    Wahrscheinlichkeitstheorie

    PDF-Datei
    Mathematische Statistik PDF-Datei (Version vom 22.02.2017)
    Stochastische Prozesse PDF-Datei (Englisch) 
    Extremwerttheorie PDF-Datei (Version vom 17.07.2015)
    Martingale (Neu!)  PDF-Datei (Version vom 07.01.2018)
    Aufgaben zur Stochastik, Teil 1 Aufgaben und Ergebnisse zur Selbstkontrolle
    Aufgaben zur Stochastik, Teil 2 Aufgaben und Ergebnisse zur Selbstkontrolle
    Aufgaben zur Stochastik, Teil 3 Aufgaben
    Aufgaben zur mathematischen Statistik Teil 1 und Teil 2

  • LaTeX-Vorlage für Bachelor- und Masterarbeiten

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  • Publikationen

    Papers and Preprints

    • Kabluchko, Z. (2018)
      An infinite-dimensional helix invariant under spherical projections.
      Preprint at arxiv.org: Link

    • Kabluchko, Z., Zaporozhets, D. (2018)
      Angles of the Gaussian simplex. 
      Preprint at arxiv.org: Link

    • Götze, F., Gusakova, A., Kabluchko, Z., Zaporozhets, D. (2018)
      Distribution of complex algebraic numbers on the unit circle.
      Preprint at arxiv.org: Link

    • Kabluchko, Z., Prochno, J.,  Vysotsky V. (2018)
      Yet another note on the arithmetic-geometric mean inequality.
      Preprint at arxiv.org: Link

    • Kabluchko, Z., Prochno, J., and Thäle, C. (2018)
      Sanov-type large deviations in Schatten classes.
      Preprint at arxiv.org: Link

    • Kabluchko, Z., Seidel, H. (2018)
      Distances between zeroes and critical points for random polynomials with i.i.d. zeroes.
      Preprint at arxiv.org: Link

    • Iksanov, A.,   Kabluchko, Z. (2018) 
      Weak convergence of the number of vertices at intermediate levels of random recursive trees. J. Appl. Probab., accepted. 
      Preprint at arxiv.org:  Link

    • Kabluchko, Z., Thäle, C., and Zaporozhets, D. (2018)
      Beta polytopes and Poisson polyhedra: f-vectors and angles.
      Preprint auf arxiv.org: Link

    • Kabluchko, Z., Prochno, J., and Thäle, C. (2018)
      Exact asymptotic volume and volume ratio of Schatten unit balls.
      Preprint auf arxiv.org: Link

    • Kabluchko, Z., Prochno, J., and Thäle, C. (2018)
      Intersection of unit balls in classical matrix ensembles.
      Preprint auf arxiv.org: Link

    • Flasche, H.,   Kabluchko, Z. (2018) 
      Real zeros of random analytic functions associated with geometries of constant curvature.  J. Theor. Probab., accepted.
      Preprint at arxiv.org: Link

    • Alsmeyer, G.,  Kabluchko, Z.,  Marynych, A. (2018) 
      Limit theorems for the least common multiple of a random set of integers. 
      Preprint at arxiv.org: Link

    • Kabluchko, Z., Marynych, A., Temesvari, D., Thäle, C. (2018) 
      Cones generated by random points on half-spheres and convex hulls of Poisson point processes. 
      Preprint at arxiv.org: Link

    • Iksanov, A.,   Kabluchko, Z. (2018) 
      A functional limit theorem for the profile of random recursive trees. Elect. Comm. Probab., 23(2018), no. 87, 1–13.
      Preprint at arxiv.org: Link
      Publisher's homepage: Link

    • Kabluchko, Z., Tent, K. (2017) 
      On weak Fraïssé limits.
      Preprint at arxiv.org: Link

    • Kabluchko, Z., Tent, K. (2017) 
      Universal-homogeneous structures are generic.
      Preprint at arxiv.org: Link

    • Kabluchko, Z., Prochno, J., and Thäle, C. (2017) 
      High-dimensional limit theorems for random vectors in l_p^n-balls. Comm. in Contemp. Math., to appear.  
      Preprint at arxiv.org: Link
      Publisher's homepage: Link

    • Flasche, H.,   Kabluchko, Z. (2017) 
      Expected number of real zeros of random Taylor series.  
      Preprint at arxiv.org: Link

    • Kabluchko, Z.,   Lifshits, M. (2017) 
      Adaptive energy saving approximation for stationary processes.  Izvestiya Math., accepted. 
      Preprint at arxiv.org: Link

    • Grote, J., Kabluchko, Z., and Thäle, C. (2017)
      Limit theorems for random simplices in high dimensions. ALEA, accepted. 
      Preprint at arxiv.org: Link

    • Kabluchko, Z., Temesvari, D. and Thäle, C. (2017)
      Expected intrinsic volumes and facet numbers of random beta-polytopes. Math. Nachr., accepted. 
      Preprint at arxiv.org: Link 
      Mathematica notebooks: Beta-Polytopes     Beta'-Polytopes

    • Kabluchko, Z.,  Zaporozhets, D. (2017) 
      Expected volumes of Gaussian polytopes, external angles, and multiple order statistics.  Trans. Amer. Math. Soc., accepted. 
      Preprint at arxiv.org: Link

    • Kabluchko, Z.,  Zaporozhets, D. (2017) 
      Absorption probabilities for Gaussian polytopes, and regular spherical simplices.   
      Preprint at arxiv.org: Link

    • Kabluchko, Z.,   Thäle, C. (2017) 
      Monotonicity of expected f-vectors for projections of regular polytopes. Proc. Amer. Math. Soc., 146(3), pp. 1295–1303, 2018.    
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Hug, D.,   Kabluchko, Z. (2016) 
      An inclusion-exclusion identity for normal cones of polyhedral sets. Mathematika, 64 (2018), 124-136.    
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Iksanov, A.,   Kabluchko, Z. (2016) 
      Functional limit theorems for Galton-Watson processes with very active immigration. Stoch. Proc. Appl., Volume 128(1), Pp. 291-305, 2018. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Kabluchko, Z.,  Vysotsky, V.,   Zaporozhets, D. (2016) 
      Convex hulls of random walks: Expected number of faces and face probabilities. Advances in Math., Vol. 320(7), pp. 595-629, 2017.
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Ibragimov, I.,  Kabluchko, Z.,   Lifshits, M. (2016) 
      Some extensions of linear approximation and prediction problems for stationary processes. Stoch. Proc. Appl., accepted. 
      Preprint at arxiv.org: Link

    • Kabluchko, Z.,  Vysotsky, V.,   Zaporozhets, D. (2016) 
      A multidimensional analogue of the arcsine law for the number of positive terms in a random walk. Bernoulli, accepted.   
      Preprint at arxiv.org: Link

    • Kabluchko, Z.,   Marynych, A.,   Sulzbach, H. (2016)
      Mode and Edgeworth expansion for the Ewens distribution and the Stirling numbers. J. Integer Sequences, 19 (2016), Article 16.8.8. 
      Preprint at arxiv.org: Link 
      Mathematica notebook: Download the notebook     The same as PDF 
      Publisher's homepage: Link

    • Alsmeyer, G.,  Kabluchko, Z.,  Marynych, A. (2016) 
      Leader election using random walks. ALEA, 13(2016), 1095-1122. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Kabluchko, Z.,   Marynych, A.,   Sulzbach, H. (2016)
      General Edgeworth expansions with applications to profiles of random trees. Ann. Appl. Probab., 27(6), pp. 3478-3524, 2017. 
      Preprint at arxiv.org (extended version): Link 
      Extended version with full proofs: Link to the PDF file 
      Publisher's homepage: Link

    • Kabluchko, Z.,   Marynych, A. (2016)
      Renewal shot noise processes in the case of slowly varying tails. Theor. Stoch. Proc., Vol.21 (37), no.2, pp.14-21, 2016. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Kabluchko, Z.,  Last, G.,  Zaporozhets, D. (2016)
      Inclusion-exclusion principles for convex hulls and the Euler relation. Discr. and Comp. Geometry, 58(2), p. 417-434, 2017. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Iksanov, A.,   Kabluchko, Z.   Marynych, A.   Shevchenko, G. (2016)
      Fractionally integrated inverse stable subordinators. Stoch. Proc. Appl., 127(1), pp. 80-106, 2017.    
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Iksanov, A., Kabluchko, Z.,  Marynych, A. (2016)
      Local universality for real roots of random trigonometric polynomials. Elect. J. Probab., Vol. 21 (2016), paper no. 63. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Dombry, C., Kabluchko, Z. (2016)
      Ergodic decompositions of stationary max-stable processes in terms of their spectral functions. Stoch. Proc. Appl., 127(6), pp. 1763-1784, 2017. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link 

    • Alsmeyer, G.,  Kabluchko, Z.,  Marynych, A. (2015) 
      A leader-election procedure using records. Ann. Probab., 45(6B), pp. 4348-4388, 2017. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Kabluchko, Z.,  Litvak, A. E.,   Zaporozhets, D. (2015) 
      Mean width of regular polytopes and expected maxima of correlated Gaussian variables.   Zap. Nauchn. Sem. POMI, 442, pp. 75-96, 2015, and J. of Math. Sci., 225(5), pp. 770-787, 2017. 
      Preprint at arxiv.org: Link 
      Publisher's homepage (Zap. Nauchn. Sem. POMI): Link  
      Publisher's homepage (J. of Math. Sci.): Link 

    • Kabluchko, Z.,  Vysotsky, V.,   Zaporozhets, D. (2015) 
      Convex hulls of random walks, hyperplane arrangements, and Weyl chambers. Geom. Funct. Anal., 27(4), p. 880-918, 2017. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link 

    • Engelke, S.,  Kabluchko, Z. (2015) 
      A characterization of the normal distribution using stationary max-stable processes. Extremes, 19(2016), pp 1-6.    
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Iksanov, A.,  Kabluchko, Z. (2015) 
      A central limit theorem and a law of the iterated logarithm for the Biggins martingale of the supercritical branching random walk. J. Appl. Probab., Volume 53(4), pp. 1178-1192, 2016.    
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Iksanov, A.,  Kabluchko, Z.,   Marynych, A. (2015) 
      Weak convergence of renewal shot noise processes in the case of slowly varying normalization. Statist. Probab. Letters, 114 (2016), pp. 67-77.    
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Grübel, R., Kabluchko, Z. (2015)
      Edgeworth expansions for profiles of lattice branching random walks. Ann. Inst. H. Poincare, 53(4), pp. 2103-2134, 2017.  
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Kabluchko, Z.,  Lifshits, M. (2015)
      Least energy approximation for processes with stationary increments. J. Theor. Probab., 30(1), pp 268-296, 2017. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Engelke, S., Kabluchko, Z. (2014)
      Max-stable processes and stationary systems of independent Lévy particles. Stoch. Proc. Appl., 125, p.4272-4299, 2015. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Dombry, C., Kabluchko, Z. (2014)
      Random tessellations associated with max-stable random fields. Bernoulli, 24(1), p. 30-52, 2018. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Grübel, R., Kabluchko, Z. (2014) 
      A functional central limit theorem for branching random walks, almost sure weak convergence, and applications to random trees. Ann. Appl. Probab., 26(6), pp. 3659-3698, 2016.    
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Kabluchko, Z., Zaporozhets, D. (2014) 
      Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls. Trans. Amer. Math. Soc., 368 (2016), pp. 8873-8899.  
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Kabluchko, Z., Klimovsky, A. (2014)
      Generalized Random Energy Model at complex temperatures. 109 pages. Submitted.
      Preprint at arxiv.org: Link

    • Kabluchko, Z., Wang, Y. (2012)
      Limiting distribution for the maximal standardized increment of a random walk. Stoch. Proc. Appl., 124(9), p.2824-2867, 2014.  
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Engelke, S., Malinowski, A., Kabluchko, Z., Schlather, M. (2012)
      Estimation of Hüsler-Reiss distributions and Brown-Resnick processes. J. Royal Statist. Soc. B., 77(1), p. 239-265, 2015. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Kabluchko, Z., Stoev, S. (2012)
      Stochastic integral representations and classification of sum- and max-infinitely divisible processes. Bernoulli, 22(1), p. 107-142, 2016. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Kabluchko, Z. (2012)
      Critical points of random polynomials with independent identically 
      distributed roots. Proc. Amer. Math. Soc., 143 (2015), 695-702.  
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Zaporozhets, D., Kabluchko, Z.  (2012)
      Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields. Zap. Nauchn. Sem. POMI 408, p.187-196, 2012 (Russian version) or Journal of Math. Sci. 199(2), p.168-173, 2014 (English version). 
      Preprint at arxiv.org: Link
      Publisher's homepage: Link (Russian version) or Link (English version). 

    • Kabluchko, Z., Zaporozhets, D. (2012) 
      Asymptotic distribution of complex zeros of random analytic functions. Ann. Probab., 42(4), p.1374-1395, 2014. 
      Preprint at arxiv.org (new, short version): Link 
      Preprint at arxiv.org (old, long version): Link 
      Publisher's homepage (short version): Link

    • Engelke, S., Kabluchko, Z., Schlather, M. (2012).
      Maxima of independent, non-identically distributed Gaussian vectors. Bernoulli, 21(1), p. 38-61, 2015. 
      Preprint at arxiv.org: Link 
      Publisher's homepage: Link

    • Kabluchko, Z., Klimovsky, A. (2012).
      Complex random energy model: Zeros and fluctuations. Probab. Th. Related Fields., 158 (2014), pp. 159-196.
      Publisher's homepage: Link
      Preprint at arxiv.org: Link

    • Kabluchko, Z., Zaporozhets, D. (2011).
      Roots of random polynomials whose coefficients have logarithmic tails. Ann. Probab., 41(5), 2013, pp. 3542-3581.
      Publisher's homepage: Link
      Preprint at arxiv.org: Link

    • Kabluchko, Z. (2011).
      Persistence and equilibria of branching populations with exponential intensity. J. Appl. Probab., 49(1), p. 226-244, 2012. 
      Preprint at arxiv.org: Link
      Publisher's homepage: Link

    • Kabluchko, Z., Padoan, S.A. (2010).
      Maxima of bivariate random vectors with strongly dependent Cauchy marginals. Unpublished.

    • Kabluchko, Z. (2010).
      The maximum of the Gaussian 1/f^alpha-noise in the case alpha<1. Unpublished.
      Preprint at arxiv.org: Link

    • Engelke, S., Kabluchko, Z., Schlather, M. (2010).
      An equivalent representation of the Brown-Resnick process. Statist. Probab. Letters, 81, p. 1150-1154, 2011.
      Publisher's homepage: Link

    • Kabluchko, Z. (2011).
      Extremes of the standardized Gaussian noise. Stoch. Processes. Appl. 121(3) p. 515-533. 
      Preprint at arxiv.org: Link
      Publisher's homepage: Link

    • Hashorva, E., Kabluchko, Z., Wübker, A. (2010).
      Extremes of independent chi-square random vectors. Extremes 15(1) p. 35-42.
      Publisher's homepage: Link

    • Kabluchko, Z. (2010).
      Distribution of levels in high-dimensional random landscapes. Ann. Appl. Probab. 22(1) p. 337-362.
      Preprint at arxiv.org: Link
      Publisher's homepage: Link

    • Kabluchko, Z. (2010).
      Functional limit theorems for sums of independent geometric Lévy processes. Bernoulli 17(3) p. 942-968.
      Preprint at arxiv. org: Link
      Publisher's homepage: Link

    • Kabluchko, Z. (2010).
      Limit laws for sums of independent random products: the lattice case.  J. Theor. Probab. 25(2), p. 424-437
      Preprint at arxiv.org: Link
      Publisher's homepage: Link

    • Kabluchko, Z. (2009).
      Extremes of independent Gaussian processes. Extremes 14(3) p. 285-310. 
      Preprint at arxiv.org: Link
      Publisher's homepage: Link

    • Kabluchko, Z., Schlather, M. (2010).
      Ergodic properties of max-infinitely divisible processes. Stoch. Processes Appl., 120, 281-295. 
      Preprint at arxiv.org: Link
      Publisher's homepage: Link

    • Kabluchko, Z. (2009).
      Limiting distributions for sums of independent random products. Not published.
      Preprint at arxiv.org: Link

    • Kabluchko, Z. (2010).
      Stationary systems of Gaussian processes. Ann. Appl. Probab., 20(6), 2295-2317.
      Preprint at arxiv.org: Link
      Publisher's homepage: Link

    • Oesting, M., Kabluchko, Z. und Schlather, M. (2012).
      Simulation of Brown-Resnick processes. Extremes, 15(1), 89-107.
      Publisher's homepage: Link

    • Hotz, T., Marnitz, P., Stichtenoth, R., Davies, L., Kabluchko, Z. and Munk, A. (2009). Locally adaptive image denoising by a statistical multiresolution criterion. Comput. Stat. Data Analysis, 56(3) p. 543-558, 2012. 
      Publisher's homepage: Link
      Preprint at arxiv.org: Link

    • Wübker, A., Kabluchko, Z. (2009).
      L2-spectral gaps, weak-reversible and very weak-reversible Markov chains.
      Preprint at arxiv.org: Link

    • Ballani, F., Kabluchko, Z., Schlather, M. (2009, appeared 2012).
      Random marked sets.  Adv. Appl. Probab., 44(3), 603-616.
      Preprint at arxiv. org: Link
      Publisher's homepage: Link

    • Kabluchko, Z. (2009).
      Extremes of space-time Gaussian processes Stoch. Processes Appl., 119, 3962-3980.
      Publisher's homepage: Link

    • Kabluchko, Z., Spodarev, E. (2009).
      Scan statistic of Lévy noises and marked empirical processes. Adv. Appl. Probab., 41, 013-037.
      Publisher's homepage: Link

    • Kabluchko, Z. (2009).
      Limiting distribution of the continuity modulus for Gaussian processes with stationary increments. Statist. Probab. Lett., 79, 953-956.
      Publisher's homepage: Link

    • Kabluchko, Z. (2009).
      Spectral representations of sum- and max-stable processes. Extremes, 12, 401-424.
      Publisher's homepage: Link

    • Kabluchko, Z., Schlather, M., de Haan, L. (2009).
      Stationary max-stable fields associated to negative definite functions. Ann. Probab. 37, 2042-2065. 
      Preprint at arxiv.org: Link
      Publisher's homepage: Link

    • Kabluchko, Z., Munk, A. (2009).
      Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays. ESAIM Probab. Stat. 13, 409-416. 
      Publisher's homepage: Link

    • Kabluchko, Z., Munk, A. (2008).
      Exact convergence rate for the maximum of standardized Gaussian increments. Elect. Comm. in Probab., 13, 302-310.
      Publisher's homepage: Link

    • Kabluchko, Z. (2007).
      Extreme-value analysis of standardized Gaussian increments. Not published. 
      Preprint at arxiv.org: Link

    • Denker, M., Kabluchko, Z. (2007).
      An Erdös-Rényi law for mixing processes. Probab. Math. Stat., 27, 139-149.
      Publisher's homepage: Link

    • Kabluchko, Z., Proskurin, D., Samojlenko, Y. (2004).
      On C*-algebras generated by deformations of the CCR. Ukr. Math. J., 56, 1813-1827.
      Publisher's homepage: Link

    • Kim, C. S., Proskurin, D., Iksanov, A., Kabluchko, Z. (2003). 
      The generalized CCR: representations and enveloping C*-algebra. Rev. Math. Phys., 15, 313-338.
      Publisher's homepage: Link

    • Kabluchko, Z. (2001). 
      On an extension of higher-dimensional noncommutative tori.
      Meth. Func. Anal. Topol., 7, 28-33. 
      Publisher's homepage: Link
      Download the PDF of the paper: Link

    Theses

    • PhD Thesis. Kabluchko, Z. (2007). 
      Extreme-Value Analysis of Self-Normalized Increments. Available at the homepage of the University of Göttingen: Link

    • Diploma Thesis. Kabluchko, Z. (2004).
      Stochastische Löwner-Evolution. University of Göttingen. 

    Reviews

    • Reviews of my papers at MathSciNet: Link
      Reviews I have written for MathSciNet: Link

    • Zentralblatt MATH: Link