S. Steinerberger

activity

20152022

most citedStochastic Neighbor Embedding separates well-separated clusters

15 citations · 45 across the 31 of their papers we have counts for

collaborators

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22 papers · 1 filter

math.CA2021★ 2 cited

A variational principle for Gaussian lattice sums

Laurent Bétermin, Markus Faulhuber, Stefan Steinerberger

We consider a two-dimensional analogue of Jacobi theta functions and prove that, among all lattices $Λ \subset R^{2}$ with fixed density, the minimal value is maximized by th…

math.CA2020

On the Logarithmic Energy of Points on S^2

Stefan Steinerberger

We revisit a classical question: how large is the minimal logarithmic energy of $n$ points on $S^{2}$ $$ \mathcal{E}_{\log}(n) = \min_{x_1, \dots, x_n \in \mathbb{S}^2} \qua…

math.CA2020

The smoothest average: Dirichlet, Fejér and Chebyshev

Noah Kravitz, Stefan Steinerberger

We are interested in the ``smoothest'' averaging that can be achieved by convolving functions $f \in ℓ^{2} (Z)$ with an averaging function $u$ . More precisely, suppose $u:…

math.CA2020

Fourier Uncertainty Principles, Scale Space Theory and the Smoothest Average

Stefan Steinerberger

Let $f \in L^{2} (R^{n})$ and suppose we are interested in computing its average at a fixed scale. This is easy: we pick the density $u$ of a probability distribution with…

math.CA2019

On the Wasserstein Distance between Classical Sequences and the Lebesgue Measure

Louis Brown, Stefan Steinerberger

We discuss the classical problem of measuring the regularity of distribution of sets of $N$ points in $T^{d}$ . A recent line of investigation is to study the cost ( $=$ mass…

math.CA2019

Positive-definite Functions, Exponential Sums and the Greedy Algorithm: a curious Phenomenon

Louis Brown, Stefan Steinerberger

We describe a curious dynamical system that results in sequences of real numbers in $[0, 1]$ with seemingly remarkable properties. Let the function $f:\mathbb{T} \rightarrow \mathbb…