Browsing by Author "Thäle, Christoph"

Now showing 1 - 3 of 3
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    Central limit theorems for the radial spanning tree
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2014) Schulte, Matthias; Thäle, Christoph
    Consider a homogeneous Poisson point process in a compact convex set in d- dimensional Euclidean space which has interior points and contains the origin. The radial spanning tree is constructed by connecting each point of the Poisson point process with its nearest neighbour that is closer to the origin. For increasing in- tensity of the underlying Poisson point process the paper provides expectation and variance asymptotics as well as central limit theorems with rates of convergence for a class of edge functionals including the total edge length.
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    Mini-Workshop: Perspectives in High-dimensional Probability and Convexity
    (Zürich : EMS Publ. House, 2017) Thäle, Christoph; Werner, Elisabeth
    Understanding the geometric structure of systems involving a huge amount of parameters is a central problem in mathematics and applied sciences today. Here, geometric and analytical ideas meet in a non-trivial way and powerful probabilistic tools play a key role in many discoveries. Two essentially independent areas of mathematics concerned with high-dimensional problems are asymptotic geometric analysis and information-based complexity. In this Mini-Workshop we brought together researchers from both fields to explore the connections and form synergies to develop new perspectives.
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    New Perspectives and Computational Challenges in High Dimensions
    (Zürich : EMS Publ. House, 2020) Prochno, Joscha; Thäle, Christoph; Werner, Elisabeth
    High-dimensional systems are frequent in mathematics and applied sciences, and the understanding of high-dimensional phenomena has become increasingly important. The mathematical subdisciplines most strongly related to such phenomena are functional analysis, convex geometry, and probability theory. In fact, a new area emerged, called asymptotic geometric analysis, which is at the very core of these disciplines and bears a number of deep connections to mathematical physics, numerical analysis, and theoretical computer science. The last two decades have seen a tremendous growth in this area. Far reaching results were obtained and various powerful techniques have been developed, which rather often have a probabilistic flavor. The purpose of this workshop was to explored these new perspectives, to reach out to other areas concerned with high-dimensional problems, and to bring together researchers having different angles on high-dimensional phenomena.