S. Steinerberger

activity

20122026

most citedEfficient Algorithms for t-distributed Stochastic Neighborhood Embedding

607 citations · 834 across the 123 of their papers we have counts for

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11 papers · 1 filter

math.SP2022

An Agmon estimate for Schrödinger operators on Graphs

Stefan Steinerberger

The Agmon estimate shows that eigenfunctions of Schrödinger operators, $- Δ ϕ + V ϕ = E ϕ$ , decay exponentially in the `classically forbidden' region where the potential exceeds the e…

math.SP2021

Quantum Entanglement and the Growth of Laplacian Eigenfunctions

Stefan Steinerberger

We study the growth of Laplacian eigenfunctions $- Δ ϕ_{k} = λ_{k} ϕ_{k}$ on compact manifolds $(M, g)$ . Hörmander proved sharp polynomial bounds on $∥ ϕ_{k} ∥_{L^{\infty}}$ which are attai…

math.SP2021★ 3 cited

A common variable minimax theorem for graphs

Ronald R. Coifman, Nicholas F. Marshall, Stefan Steinerberger

Let $G = {G_{1} = (V, E_{1}), \dots, G_{m} = (V, E_{m})}$ be a collection of $m$ graphs defined on a common set of vertices $V$ but with different edge sets $E_{1}, \dots, E_{m}$ .…

math.SP2021

The product of two high-frequency Graph Laplacian eigenfunctions is smooth

Stefan Steinerberger

In the continuous setting, we expect the product of two oscillating functions to oscillate even more (generically). On a graph $G = (V, E)$ , there are only $∣ V ∣$ eigenvectors of the L…

math.SP2018★ 3 cited

On Pointwise Products of Elliptic Eigenfunctions

Jianfeng Lu, Stefan Steinerberger

We consider eigenfunctions of Schrödinger operators on a $d -$ dimensional bounded domain $Ω$ (or a $d -$ dimensional compact manifold $Ω$ ) with Dirichlet conditions. These operators g…

math.SP2017

Spectral Limitations of Quadrature Rules and Generalized Spherical Designs

Stefan Steinerberger

We study manifolds $M$ equipped with a quadrature rule $\int_{M} ϕ (x) d x ≃ i = 1 \sum n a_{i} ϕ (x_{i}) .$ We show that $n -$ point quadrature rules with nonnegative weights on…