Document Type
Lecture
Publication Date
10-17-2008
Abstract
In this talk, we will discuss results about the asymptotic behavior of certain point configurations called Greedy Energy (GE) points. These points form a sequence generated by means of a greedy algorithm, which is an energy-minimizing construction. The notion of energy that we consider comes from the Riesz potentials �� = 1/��ˢ in ℝᵖ, where �� > 0 and �� denotes the Euclidean distance. It turns out that for certain values of the parameter ��, these configurations behave asymptotically like Minimal Energy (ME) configurations. This property will also be discussed in more abstract contexts like locally compact Hausdorff spaces. For other values of ��, GE and ME configurations exhibit different asymptotic properties, for example, for �� > 1 on Jordan curves or arcs. We will discuss second-order asymptotics on the unit circle, distribution, and weighted Riesz potentials on unit spheres. This is joint work with E. Sa.
Relational Format
presentation
Recommended Citation
Lopez, Abey, "Asymptotics of Greedy Energy Sequences" (2008). Analysis Seminar. 41.
https://egrove.olemiss.edu/math_analysis/41
