TY - JOUR
T1 - Concentration of measures supported on the cube
AU - Klartag, Bo’az
N1 - Publisher Copyright:
© 2014, Hebrew University Magnes Press.
PY - 2014/10
Y1 - 2014/10
N2 - We prove a log-Sobolev inequality for a certain class of log-concave measures in high dimension. These are the probability measures supported on the unit cube [0, 1]n ⊂ ℝn whose density takes the form exp(−ψ), where the function ψ is assumed to be convex (but not strictly convex) with bounded pure second derivatives. Our argument relies on a transportation-cost inequality á la Talagrand.
AB - We prove a log-Sobolev inequality for a certain class of log-concave measures in high dimension. These are the probability measures supported on the unit cube [0, 1]n ⊂ ℝn whose density takes the form exp(−ψ), where the function ψ is assumed to be convex (but not strictly convex) with bounded pure second derivatives. Our argument relies on a transportation-cost inequality á la Talagrand.
UR - http://www.scopus.com/inward/record.url?scp=84886740017&partnerID=8YFLogxK
U2 - 10.1007/s11856-013-0072-1
DO - 10.1007/s11856-013-0072-1
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AN - SCOPUS:84886740017
SN - 0021-2172
VL - 203
SP - 59
EP - 80
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -