Large deviations and isoperimetry over convex probability measures with heavy tails

By Sergey G. Bobkov. 2007

71 citations recorded by the source corpus.

Large deviations and isoperimetric inequalities are considered for probability distributions, satisfying convexity conditions of the Brunn-Minkowski-type

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ee224d73a92b15a9d02a1f6d57484ab80fee1205

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In Applied Mathematics

In Numerical Analysis

In Statistics and Probability

Citations in the corpus

Convex bodies and norms associated to convex measures (2010, unknown): “[11]), f (x) ≤ C 1 + |x |n+α , α = − 1 κ .”
Sharp Isoperimetric Inequalities and Model Spaces for Curvature-Dimension-Diameter Condition (2011, methodology): “hich however does not extend to the full Riemannian setting (cf. [59]), is by reducing to the onedimensional case treated in Corollary 3.2 using the localization technique of [64, 38, 44] (e.g. as in [17, 18]). When ρ 6= 0 and q < ∞, this reduction seems new and of independent interest, but we le”
Complemented Brunn–Minkowski inequalities and isoperimetry for homogeneous and non-homogeneous measures (2013, unknown): “[2, 1] and the references therein), we may rewrite the isoperimetric inequalities obtained in the previous sections as Sobolev-type inequalities.”
Weighted poincaré-type inequalities for cauchy and other convex measures (2009, background): “Moreover, as recently shown in [5], the constant C can be made dependent on β , but independent of q .”
Reverse Brunn–Minkowski and reverse entropy power inequalities for convex measures (2011, background): “1.10), announced in the introductory section. 9 4 Entropy and maximum of density Any convex probability measure has a bounded density, i.e., the L∞-norm kfk = sup x f(x) of the density fis ﬁnite (cf. [9]). For suﬃciently convex probability measures, the entropy may be related to kfk via the followin”
Applications of Stein's method for concentration inequalities (2009, background): “The papers [2, 14, 20, 28] deal with tails between exponential and Gaussian and [1, 4] deal with subexponential tails.”
Beyond traditional Curvature-Dimension I: new model spaces for isoperimetric and concentration inequalities in negative dimension (2014, methodology): “The ﬁrst assertion was obtained by Bobkov in [9, Section 8] in the Euclidean setting.”