Interplay between Stochastic Partial Differential Equations and Quantum Field Theory on Curved Backgrounds
De Claudio Dappiaggi
Apparaît dans la collection : Jean-Morlet Chair 2020 - Workshop: Discrepancy Theory and Applications - Part 1 / Chaire Jean-Morlet 2020 - Workshop : Théorie de la discrépance et applications - Part 1
In this talk I will report on recent progress on two different problems in discrepancy theory. In the first part I will present a recent extension of the notion of jittered sampling to arbitrary partitions of the unit cube. In this joint work with Markus Kiderlen from Aarhus, we introduce the notion of a uniformly distributed triangular array. Moreover, we show that the expected Lp-discrepancy of a point sample generated from an arbitrary equi volume partition of the unit cube is always strictly smaller than the expected Lp-discrepancy of a set of N uniform random samples for p > 1. The second part of the talk is dedicated to greedy energy minimization. I will give a new characterisation of the classical van der Corput sequence in terms of a minimization problem and will discuss various related open questions.