Steven M. Heilman

activity

20092026

most citedLocalized Eigenfunctions: Here You See Them, There You Don't

20 citations · 42 across the 28 of their papers we have counts for

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16 papers · 1 filter

math.PR2025

A Fourier approach to Levine's hat puzzle

Steven Heilman, Omer Tamuz

We consider Lionel Levine's notorious hat puzzle with two players. Each player has a stack of hats on their head, and each hat is chosen independently to be either black or white.…

math.PR2023

Three Candidate Plurality is Stablest for Correlations at most 1/10

Steven Heilman

We prove the three candidate Plurality is Stablest Conjecture of Khot-Kindler-Mossel-O'Donnell from 2005 for correlations $ρ$ satisfying $- 1/43 < ρ < 1/10$ : the Plurality function is t…

math.PR2022

Hyperstable Sets with Voting and Algorithmic Hardness Applications

Steven Heilman

The noise stability of a Euclidean set $A$ with correlation $ρ$ is the probability that $(X, Y) \in A \times A$ , where $X, Y$ are standard Gaussian random vectors with correlation $ρ\i…

math.PR2022★ 2 cited

Convex Cylinders and the Symmetric Gaussian Isoperimetric Problem

Steven Heilman

Let $Ω$ be a measurable Euclidean set in $R^{n}$ that is symmetric, i.e. $Ω = - Ω$ , such that $Ω \times R$ has the smallest Gaussian surface area among all measurable…

math.PR2022

Dimension-Free Noninteractive Simulation from Gaussian Sources

Steven Heilman, Alex Tarter

Let $X$ and $Y$ be two real-valued random variables. Let $(X_{1}, Y_{1}), (X_{2}, Y_{2}), \dots$ be independent identically distributed copies of $(X, Y)$ . Suppose there are two player…

math.PR2021★ 1 cited

A Variational Proof of Robust Gaussian Noise Stability

Steven Heilman

Using the calculus of variations, we prove that a Euclidean set of fixed Gaussian measure that nearly maximizes Gaussian noise stability is close to a half space. The main result p…