FB 6 Mathematik/Informatik

Institut für Mathematik


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WS 2017/2018

24.11.2017 um 12:00 Uhr in Raum 69/118

Martin Wendler (Universität Greifswald)

Convergence of U-statistics indexed by a random walk

27.11.2017 um 14:15 Uhr in Raum 69/E23

Robert Kunsch (Universität Osnabrück)

Optimal sample size selection for Monte Carlo integration at a priori unknown dispersion

Abstract: We aim to compute the expected value of a random variable from i.i.d. samples. Under certain assumptions it is possible to select a sample size on ground of a variance estimation, or - more generally - an estimation on a central absolute $p$-moment, such that we can guarantee a small absolute error with high probability. The expected cost of the method depends on the dispersion of the random variable, namely the p-moment, which can be arbitrarily large. Lower bounds show that - up to constants - the cost of the algorithm is optimal in terms of accuracy, confidence level and dispersion of the particular input random variable. Problems of this type are uncommon for numerical analysis where the complexity of an integration problem is usually given by the minimal number of samples needed in order to guarantee a small error for the whole input class. This quantity would be infinite for the discussed setting.
Joint work with Erich Novak (Jena) and Daniel Rudolf (Göttingen) 

01.02.2017 um 14:00 Uhr in Raum 32/131

Benedikt Jahnel (WIAS Berlin)

Continuum percolation for Cox point processes

Abstract: I will present results on continuum percolation for Cox point processes, that is, Poisson point processes driven by random intensity measures. For this, sufficient conditions for the existence of non-trivial sub- and super-critical percolation regimes based on the notion of stabilization will be exhibited. Moreover, in the talk I will discuss asymptotic expressions for the percolation probability in large connection radius, large density and coupled regimes. In some regimes, we find universality, whereas in others, a sensitive dependence on the underlying random intensity measure survives. This is joint work with Christian Hirsch (LMU Munich) and Elie Calie (Orange SA Paris).