Zakhar Kabluchko Dissertation Proposal

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Publications Prof. Zakhar Kabluchko

Papers and Preprints

  • Flasche, H.,   Kabluchko, Z. (2018)
    Real zeros of random analytic functions associated with geometries of constant curvature.  
    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.
    Preprint at arxiv.org: 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.   
    Preprint at arxiv.org: Link
  • Grote, J., Kabluchko, Z., and Thäle, C. (2017)
    Limit theorems for random simplices in high dimensions.
    Preprint at arxiv.org: Link
  • Kabluchko, Z., Temesvari, D. and Thäle, C. (2017)
    Expected intrinsic volumes and facet numbers of random beta-polytopes. Submitted.
    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.   
    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.   
    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 notebookThe 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: 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.
  • Kim, C. S., Proskurin, D., Iksanov, A., Kabluchko, Z. (2003).
    The generalized CCR: representations and enveloping C*-algebra. Rev. Math. Phys., 15, 313-338.
  • Kabluchko, Z. (2001).
    On an extension of higher-dimensional noncommutative tori.
    Meth. Func. Anal. Topol., 7, 28-33.
    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

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