Metric and Mixing Sufficient Conditions for Concentration of Measure
Abstract
We derive sufficient conditions for a family
(
X
n
,
ρ
n
,
P
n
)
of metric probability spaces to have the measure concentration property. Specifically, if the sequence
{
P
n
}
of probability measures satisfies a strong mixing condition (which we call
η
-mixing) and the sequence of metrics
{
ρ
n
}
is what we call
Ψ
-dominated, we show that
(
X
n
,
ρ
n
,
P
n
)
is a normal Levy family. We establish these properties for some metric probability spaces, including the possibly novel
X=[0,1]
,
ρ
n
=
ℓ
1
case.