TY - JOUR
T1 - Isoperimetric and analytic inequalities for log-concave probability measures
AU - Bobkov, S. G.
PY - 1999/10
Y1 - 1999/10
N2 - We discuss an approach, based on the Brunn-Minkowski inequality, to isoperimetric and analytic inequalities for probability measures on Euclidean space with logarithmically concave densities. In particular, we show that such measures have positive isope rimetric constants in the sense of Cheeger and thus always share Poincaré-type inequalities. We then describe those log-concave measures which satisfy isoperimetric inequalities of Gaussian type. The results are precised in dimension 1.
AB - We discuss an approach, based on the Brunn-Minkowski inequality, to isoperimetric and analytic inequalities for probability measures on Euclidean space with logarithmically concave densities. In particular, we show that such measures have positive isope rimetric constants in the sense of Cheeger and thus always share Poincaré-type inequalities. We then describe those log-concave measures which satisfy isoperimetric inequalities of Gaussian type. The results are precised in dimension 1.
KW - Isoperimetric constants
KW - Isoperimetric inequalities
KW - Logarithmic Sobolev inequalities
KW - Logarithmically concave measures
KW - Poincaré-type inequalities
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U2 - 10.1214/aop/1022874820
DO - 10.1214/aop/1022874820
M3 - Article
AN - SCOPUS:0033233673
SN - 0091-1798
VL - 27
SP - 1903
EP - 1921
JO - Annals of Probability
JF - Annals of Probability
IS - 4
ER -