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WS 2024/25

26.11.2024 um 13:00 Uhr in 69/E15

Prof. Dr. Michael Gnewuch (Universität Osnabrück)

"Upper bounds for the dispersion of sample points"

The (volume) dispersion with respect to axis parallel boxes is a measure of the uniformity of sample point sets. Given an n point set P in the d dimensional unit cube, the dispersion is simply the volume of the largest axis parallel box that does not contain any point of P. We are interested in the best possible dispersion of any n point set in dimension d as a function of both parameters n and d. Recently two nice (and short!) papers appeared that improved on the previously known results. This measure is related to the metric dispersion, also know as "fill- distance", and to the classical discrepancy with respect to axis parallel boxes. In two informal chalkboard talks we want to discuss the main ideas of the paper of Sasha Litvak and E. Arman (Journal of Complexity 2024), which deals with upper bounds, and of the paper by M. Trödler, J. Volec and Jan Vybíral (European Journal of Combinatorics 2024), which deals with lower bounds. 

03.12.2024 um 13:00 Uhr in 69/E15

Prof. Dr. Michael Gnewuch (Universität Osnabrück)

"Lower bounds for the smallest possible dispersion of n points in dimension d"

The (volume) dispersion with respect to axis parallel boxes is a measure of the uniformity of sample point sets. Given an n point set P in the d dimensional unit cube, the dispersion is simply the volume of the largest axis parallel box that does not contain any point of P. We are interested in the best possible dispersion of any n point set in dimension d as a function of both parameters n and d. Recently two nice (and short!) papers appeared that improved on the previously known results. This measure is related to the metric dispersion, also know as "fill- distance", and to the classical discrepancy with respect to axis parallel boxes. In two informal chalkboard talks we want to discuss the main ideas of the paper of Sasha Litvak and E. Arman (Journal of Complexity 2024), which deals with upper bounds, and of the paper by M. Trödler, J. Volec and Jan Vybíral (European Journal of Combinatorics 2024), which deals with lower bounds.