Zobrazeno 1 - 10
of 22
pro vyhledávání: '"Steven Heilman"'
Autor:
Steven Heilman, Alex Tarter
Publikováno v:
Forum of Mathematics, Sigma, Vol 9 (2021)
Using the calculus of variations, we prove the following structure theorem for noise-stable partitions: a partition of n-dimensional Euclidean space into m disjoint sets of fixed Gaussian volumes that maximise their noise stability must be $(m-1)$-di
Externí odkaz:
https://doaj.org/article/01342b8010b74594aa52e4e2065aa58e
Autor:
Steven Heilman
We demonstrate a method for proving precise concentration inequalities in uniformly random trees on $n$ vertices, where $n\geq1$ is a fixed positive integer. The method uses a bijection between mappings $f\colon\{1,\ldots,n\}\to\{1,\ldots,n\}$ and do
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d1f54259f97a778255247843925d8d43
Publikováno v:
Transactions of the American Mathematical Society. 369:4843-4863
We study contraction under a Markov semi-group and influence bounds for functions in L 2 L^2 tail spaces, i.e., functions all of whose low level Fourier coefficients vanish. It is natural to expect that certain analytic inequalities are stronger for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::541972e748fda0c2b0f87a79f7cc4269
https://doi.org/10.1090/tran/6916
https://doi.org/10.1090/tran/6916
Autor:
Steven Heilman
Publikováno v:
Notices of the American Mathematical Society. 68:1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b7904d1c908e90910278b44d2f88bcdc
https://doi.org/10.1090/noti2251
https://doi.org/10.1090/noti2251
Publikováno v:
Israel Journal of Mathematics. 213:33-53
The Standard Simplex Conjecture and the Plurality is Stablest Conjecture are two conjectures stating that certain partitions are optimal with respect to Gaussian and discrete noise stability respectively. These two conjectures are natural generalizat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::22381f713339b05941d8f7366a17a234
https://doi.org/10.1007/s11856-016-1320-y
https://doi.org/10.1007/s11856-016-1320-y
Autor:
Steven Heilman
It is shown that $m$ disjoint sets with fixed Gaussian volumes that partition $\mathbb{R}^{n}$ with minimum Gaussian surface area must be $(m-1)$-dimensional. This follows from a second variation argument using infinitesimal translations. The special
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f6adceeaa1a95e75d14ad87e4694f5b5
http://arxiv.org/abs/1805.10203
http://arxiv.org/abs/1805.10203
Autor:
Steven Heilman
We prove the endpoint case of a conjecture of Khot and Moshkovitz related to the Unique Games Conjecture, less a small error. Let $n\geq2$. Suppose a subset $\Omega$ of $n$-dimensional Euclidean space $\mathbb{R}^{n}$ satisfies $-\Omega=\Omega^{c}$ a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ec604f83ee5cc450d03501e0c49d0351
http://arxiv.org/abs/1708.00917
http://arxiv.org/abs/1708.00917
Autor:
Steven Heilman
Let $\Omega\subset\mathbb{R}^{n+1}$ have minimal Gaussian surface area among all sets satisfying $\Omega=-\Omega$ with fixed Gaussian volume. Let $A=A_{x}$ be the second fundamental form of $\partial\Omega$ at $x$, i.e. $A$ is the matrix of first ord
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d621bf35d5b2f126e7a3a3cc93bd63fe
http://arxiv.org/abs/1705.06643
http://arxiv.org/abs/1705.06643
Publikováno v:
Discrete & Computational Geometry. 50:263-305
It is shown that every measurable partition $$\{A_1,\ldots , A_k\}$${A1,ź,Ak} of $$\mathbb R ^3$$R3 satisfies $$\begin{aligned} \sum _{i=1}^k\big \Vert \int _{A_i} x\mathrm{{e}}^{-\frac{1}{2}\Vert x\Vert _2^2}\mathrm{{d}}x\big \Vert _2^2\leqslant 9\
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b32495bea87e6d4399ebdb950ff175e0
https://doi.org/10.1007/s00454-013-9530-0
https://doi.org/10.1007/s00454-013-9530-0
Autor:
Robert S. Strichartz, Steven Heilman
Publikováno v:
Fractals. 18:1-34
Consider a family of bounded domains Ωt in the plane (or more generally any Euclidean space) that depend analytically on the parameter t, and consider the ordinary Neumann Laplacian Δt on each of them. Then we can organize all the eigenfunctions in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bf033415379d6dce37d32cc105fdd7fa
https://doi.org/10.1142/s0218348x10004750
https://doi.org/10.1142/s0218348x10004750