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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19 papers · 1 filter

math.AP2022

Magnetic Schrödinger operators and landscape functions

Jeremy G. Hoskins, Hadrian Quan, Stefan Steinerberger

We study localization properties of low-lying eigenfunctions of magnetic Schrödinger operators $\frac{1}{2} (- i \nabla - A (x))^{2} ϕ + V (x) ϕ = λ ϕ,$ where $V:Ω\rightarrow…

math.AP2021★ 1 cited

Effective Bounds for the Decay of Schrödinger Eigenfunctions and Agmon bubbles

Stefan Steinerberger

We study solutions of $- Δ u + V u = λ u$ on $R^{n}$ . Such solutions localize in the `allowed' region ${x \in R^{n} : V (x) \leq λ}$ and decay exponentially i…

math.AP2021

An upper bound on the Hot Spots constant

Stefan Steinerberger

Let $D \subset R^{d}$ be a bounded, connected domain with smooth boundary and let $- Δ u = μ_{1} u$ be the first nontrivial eigenfunction of the Laplace operator with Neumann bo…

math.AP2021

A Pointwise Inequality for Derivatives of Solutions of the Heat Equation in Bounded Domains

Stefan Steinerberger

Let $u (t, x)$ be a solution of the heat equation in $R^{n}$ . Then, each $k -$ th derivative also solves the heat equation and satisfies a maximum principle, the largest $k -$ th…

math.AP2020

Regularized Potentials of Schrödinger Operators and a Local Landscape Function

Stefan Steinerberger

We study localization properties of low-lying eigenfunctions $$(-Δ+V) ϕ= λϕ\qquad \mbox{in}~Ω$$ for rapidly varying potentials $V$ in bounded domains $Ω \subset R^{d}$ . Filoc…

math.AP2020

Non-Convex Planar Harmonic Maps

Shahar Z. Kovalsky, Noam Aigerman, Ingrid Daubechies +3

We formulate a novel characterization of a family of invertible maps between two-dimensional domains. Our work follows two classic results: The Radó-Kneser-Choquet (RKC) theorem, w…