Stefan Steinerberger

activity

20232026

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12 papers · 1 filter

math.CA2025

Many critical points for discrete Riesz energy on $T^{2}$

François Clément, Stefan Steinerberger

It is widely believed that the energy functional $E_{p} : (S^{2})^{n} \to R$ $E_{p} = i \neq = j i , j = 1 \sum n \frac{1}{∥ x _{i} - x _{j} ∥ ^{p}}$ has a number of cr…

math.CO2025

Balanced Stick Breaking

François Clément, Stefan Steinerberger

Consider an infinite sequence $(x_{k})_{k = 1}^{\infty}$ on the unit circle $S^{1}$ . We may interpret the first $n$ elements $(x_{k})_{k = 1}^{n}$ as places where the `circular stic…

math.OC2025

Robust Online Sampling from Possibly Moving Target Distributions

François Clément, Stefan Steinerberger

We suppose we are given a list of points $x_{1}, \dots, x_{n} \in R$ , a target probability measure $μ$ and are asked to add additional points $x_{n + 1}, \dots, x_{n + m}$ so that…

eess.SP2025

Time-Frequency Filtering Meets Graph Clustering

Marcelo A. Colominas, Stefan Steinerberger, Hau-Tieng Wu

We show that the problem of identifying different signal components from a time-frequency representation can be equivalently phrased as a graph clustering problem: given a graph $G…

math.DS2025

Superpolynomial convergence in the Riemann Rearrangement Theorem

Stefan Steinerberger

Let $x \in R$ be arbitrary and consider the `greedy' approximation of $x$ by signed harmonic sums: given $a_{n} = \sum_{k \leq n} ε_{k} / k$ with $\varepsilon_k \in \l…

math.CA2025

Potential Theory and the Boundary of Combinatorial Graphs

Stefan Steinerberger

Let $G = (V, E)$ be a finite, connected graph. We investigate a notion of boundary $\partial G \subseteq V$ and argue that it is well behaved from the point of view of potential theor…

math.NT2025

On an iterated arithmetic function problem of Erdos and Graham

Stefan Steinerberger

Erdős and Graham define $g (n) = n + ϕ (n)$ and the iterated application $g_{k} (n) = g (g_{k - 1} (n))$ . They ask for solutions of $g_{k + r} (n) = 2 g_{k} (n)$ and observe $g_{k+2}(10) = 2 g_…

math.CO2025

Many antipodes implies many neighbors

Stefan Steinerberger

Suppose ${x_{1}, \dots, x_{n}} \subset R^{2}$ is a set of $n$ points in the plane with diameter $\leq 1$ , meaning $∥ x_{i} - x_{j} ∥ \leq 1$ for all $1 \leq i, j \leq n$ …

math.NT2025

On the largest singular vector of the Redheffer matrix

François Clément, Stefan Steinerberger

The Redheffer matrix $A_{n} \in R^{n \times n}$ is defined by setting $A_{ij} = 1$ if $j = 1$ or $i$ divides $j$ and 0 otherwise. One of its many interesting properties is tha…

math.CO2025

Small gaps in the Ulam sequence

François Clément, Stefan Steinerberger

The Ulam sequence, described by Stanislaw Ulam in the 1960s, starts $1, 2$ and then iteratively adds the smallest integer that can be uniquely written as the sum of two distinct ear…

math.PR2025

Regularizing random points by deleting a few

Dmitriy Bilyk, Stefan Steinerberger

It is well understood that if one is given a set $X \subset [0, 1]$ of $n$ independent uniformly distributed random variables, then $$ \sup_{0 \leq x \leq 1} \left| \frac{\# X \cap…

math.MG2025

A Stability Version of the Jones Opaque Set Inequality

Stefan Steinerberger

Let $Ω \subset R^{2}$ be a bounded, convex set. A set $O \subset R^{2}$ is an opaque set (for $Ω$ ) if every line that intersects $Ω$ also intersects $O$ . What is the m…

Many critical points for discrete Riesz energy on T2

Balanced Stick Breaking

Robust Online Sampling from Possibly Moving Target Distributions

Time-Frequency Filtering Meets Graph Clustering

Superpolynomial convergence in the Riemann Rearrangement Theorem

Potential Theory and the Boundary of Combinatorial Graphs

On an iterated arithmetic function problem of Erdos and Graham

Many antipodes implies many neighbors

On the largest singular vector of the Redheffer matrix

Small gaps in the Ulam sequence

Regularizing random points by deleting a few

A Stability Version of the Jones Opaque Set Inequality

Many critical points for discrete Riesz energy on $T^{2}$