S. Steinerberger

activity

20152026

most citedStochastic Neighbor Embedding separates well-separated clusters

15 citations · 51 across the 47 of their papers we have counts for

collaborators

Showing 2019 · math.APShow all

4 papers · 2 filters

math.AP2019

Towards Optimal Gradient Bounds for the Torsion Function in the Plane

Jeremy G. Hoskins, Stefan Steinerberger

Let $Ω \subset R^{2}$ be a bounded, convex domain and let $u$ be the solution of $- Δ u = 1$ vanishing on the boundary $\partial Ω$ . The estimate $$ \| \nabla u\|_{L^{\infty}(Ω…

math.AP2019

A Nonlocal Transport Equation Modeling Complex Roots of Polynomials under Differentiation

Sean O'Rourke, Stefan Steinerberger

Let $p_{n} : C \to C$ be a random complex polynomial whose roots are sampled i.i.d. from a radial distribution $u (r) r d r$ in the complex plane. A natural que…

math.AP2019

Optimal Trapping of Brownian Motion: A Nonlinear Analogue of the Torsion Function

Jianfeng Lu, Stefan Steinerberger

We study the problem of maximizing the expected lifetime of drift diffusion in a bounded domain. More formally, we consider the PDE \[ - Δu + b(x) \cdot \nabla u = 1 \qquad \mbox{i…

math.AP2019

Hot Spots in Convex Domains are in the Tips (up to an Inradius)

Stefan Steinerberger

Let $Ω \subset R^{2}$ be a bounded, convex domain and let $- Δ ϕ_{1} = μ_{1} ϕ_{1}$ be the first nontrivial Laplacian eigenfunction with Neumann boundary conditions. The Hot Spots co…