Isoperimetry and Gaussian analysis

By M. Ledoux. 1996

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Citations in the corpus

Fastfood: Approximate Kernel Expansions in Loglinear Time (2014, methodology): “Then the following holds (Ledoux, 1996, Inequality 2.9): Theorem 13 Assume that f : R d → R is Lipschitz continuous with constant L and let g ∼ N (0 , 1 ) be drawn from a d -dimensional Normal distribution.”
Concentration inequalities using the entropy method (2003, methodology): “A novel way of deriving powerful inequalities, the “entropy method”, based on logarithmic Sobolev inequalities, was developed by Ledoux [17],[16], Bobkov and Ledoux [3], Massart [24], Rio [28], and Bousquet [5] for proving sharp concentration bounds for maxima of empirical processes.”
Beyond simple models of self-control to circuit-based accounts of adolescent behavior. (2015, background): “The fight-or-flight response to a perceived threat is a physiological reaction (LeDoux 1996).”
An asymmetric affine Pólya–Szegö principle (2012, background): “The natural problem to find a sharp Lp analogue of inequality (44) was solved by Ledoux [43] for p = 1 and recently by Del Pino and Dolbeault [27] for 1 p n: If f ∈W 1,p(Rn), with 1 ≤ p n, such that ‖f‖p = 1, then (45) ∫ Rn |f |p log |f | dx ≤ n p log (bn,p ‖∇f‖p) , where the optimal constant ”
On Some Inequalities for Gaussian Measures (2002, background): “Some examples of applications of Gaussian measures can be found in monographs [4, 18, 20] and [23].”
Concentration and deviation inequalities in infinite dimensions via covariance representations (2002, background): “Deviation and concentration have attracted a lot of attention in recent years well summarized in [17, 18] where the reader will find up-to-date information, precise references and credit.”
Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance (2011, unknown): “According to the Gaussian isoperimetric inequality (see [20]), for all λ > 0 and ε > 0, μ(λK + εB) ≥ Φ ( λ+Φ(μ(εB)) )”
Sharp uncertainty principles on Riemannian manifolds: the influence of curvature (2013, background): “Theorem 1.2 can be included into the best constant program initiated by Aubin [4], and studied by Ledoux [30], Cheeger and Colding [12], Druet, Hebey and Vaugon [16], do Carmo and Xia [15], Minerbe [32], Li and Wang [31], etc.”
A two-sided estimate for the Gaussian noise stability deficit (2013, methodology): “By plugging the result of the theorem and of the above corollary into Ledoux’s method, described in [17] (in the discussion following proposition 8.”
Robust Optimality of Gaussian Noise Stability (2012, methodology): “By applying Ledoux’s result [32] connecting Borell’s inequality with the Gaussian isoperimetric inequality, Theorem 1.”
Lower tail probabilities for Gaussian processes (2004, background): “Hence, it follows from the deviation estimate for Gaussian process [see Ledoux and Talagrand (1991)] that”