On the oscillation rigidity of a lipschitz function on a high-dimensional flat torus

Dmitry Faifman; Bo'az Klartag; Vitali Milman

doi:10.1007/978-3-319-09477-9_10

On the oscillation rigidity of a lipschitz function on a high-dimensional flat torus

Dmitry Faifman
, Bo'az Klartag
, Vitali Milman

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

Given an arbitrary 1-Lipschitz function f on the torus Tⁿ, we find a k-dimensional subtorus M ⊆ Tⁿ, parallel to the axes, such that the restriction of f to the subtorus M is nearly a constant function. The k-dimensional subtorus M is selected randomly and uniformly. We show that when k ≤ c log n/(log log n + log 1/ε), the maximum and the minimum of f on this random subtorus M differ by at most ε, with high probability.

Original language	English GB
Pages (from-to)	123-131
Number of pages	9
Journal	Lecture Notes in Mathematics
Volume	2116
DOIs	https://doi.org/10.1007/978-3-319-09477-9_10
State	Published - 2014

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/978-3-319-09477-9_10

Cite this

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abstract = "Given an arbitrary 1-Lipschitz function f on the torus Tn, we find a k-dimensional subtorus M ⊆ Tn, parallel to the axes, such that the restriction of f to the subtorus M is nearly a constant function. The k-dimensional subtorus M is selected randomly and uniformly. We show that when k ≤ c log n/(log log n + log 1/ε), the maximum and the minimum of f on this random subtorus M differ by at most ε, with high probability.",

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N2 - Given an arbitrary 1-Lipschitz function f on the torus Tn, we find a k-dimensional subtorus M ⊆ Tn, parallel to the axes, such that the restriction of f to the subtorus M is nearly a constant function. The k-dimensional subtorus M is selected randomly and uniformly. We show that when k ≤ c log n/(log log n + log 1/ε), the maximum and the minimum of f on this random subtorus M differ by at most ε, with high probability.

AB - Given an arbitrary 1-Lipschitz function f on the torus Tn, we find a k-dimensional subtorus M ⊆ Tn, parallel to the axes, such that the restriction of f to the subtorus M is nearly a constant function. The k-dimensional subtorus M is selected randomly and uniformly. We show that when k ≤ c log n/(log log n + log 1/ε), the maximum and the minimum of f on this random subtorus M differ by at most ε, with high probability.

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U2 - 10.1007/978-3-319-09477-9_10

DO - 10.1007/978-3-319-09477-9_10

M3 - مقالة

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SP - 123

EP - 131

JO - Lecture Notes in Mathematics

JF - Lecture Notes in Mathematics

ER -

On the oscillation rigidity of a lipschitz function on a high-dimensional flat torus

Abstract

ASJC Scopus subject areas

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