Isoperimetry for Product of Probability Measures: Recent Results
2010, v.16, №4, 617-634
We present recent results on the isoperimetric problem for product of probability measures. For distributions with tails between exponential and Gaussian we state a dimension free result. We sketch its proof that relies on a functional inequality of Poincar'e type and on a semi-group argument. Also, we give isoperimetric and concentration results, depending on the dimension, for measures with heavy tails.
Keywords: isoperimetry,Poincare type inequality,concentration of measurephenomenon,heavy tails distributions,Gaussian measure