TY - JOUR

T1 - On the oscillation rigidity of a lipschitz function on a high-dimensional flat torus

AU - Faifman, Dmitry

AU - Klartag, Bo'az

AU - Milman, Vitali

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2014.

PY - 2014

Y1 - 2014

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.

UR - http://www.scopus.com/inward/record.url?scp=84921500726&partnerID=8YFLogxK

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

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

M3 - מאמר

AN - SCOPUS:84921500726

VL - 2116

SP - 123

EP - 131

JO - Lecture Notes in Mathematics

JF - Lecture Notes in Mathematics

SN - 0075-8434

ER -