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
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AN - SCOPUS:84921500726
VL - 2116
SP - 123
EP - 131
JO - Lecture Notes in Mathematics
JF - Lecture Notes in Mathematics
SN - 0075-8434
ER -