Invariances in variance estimates

By Franck Barthe, Dario Cordero-Erausquin. 2011

58 citations recorded by the source corpus.

We provide variants and improvements of the Brascamp–Lieb variance inequality which takes into account the invariance properties of the underlying measure. This is applied to spectral gap estimates for log‐concave measures with many symmetries and to non‐interacting conservative spin systems.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2fba32489879fc109d94c05d418f09ef327c081b

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In Applied Mathematics

1. Emanuel Milman
2. A. V. Kolesnikov
3. Kolesnikov Alexander
4. Milman Emanuel
5. Zoltán M. Balogh
6. Alexandru Krist'aly
7. Joaquim Martín
8. Mario Milman

In Statistics and Probability

1. Kolesnikov Alexander
2. Milman Emanuel
3. A. V. Kolesnikov
4. Emanuel Milman

Citations in the corpus

• Transport Inequalities for Log-concave Measures, Quantitative Forms, and Applications (2015, unknown): “ constant c>0. We can replace h(µV )2 by λ(µV ), in view of (11). One can derive a similar result using H¨ormander’s L2-method, but with a different centering condition of the form R ∇gdµV = 0 (see [2]). We should add, as apparent from the proof, that the convexity of V is not really needed in Pro”
• Local Lp-Brunn-Minkowski inequalities for p<1 (2017, background): “ ≥ (1 −λ)V (K0) p n + λV(K1) p n n p ∀λ ∈ [0,1]. 6.3 Examples Of course, using the known estimates on CPoin(K) which improve over the general (6.5) for various classes of convex bodies K (see e.g. [34, 3, 32, 37, 38]), one may obtain an improved estimate for p above. It will be instructive in this ”
• Local $L^p$-Brunn-Minkowski inequalities for $p<1$ (2017, background): “[30, 3, 28, 32, 33]), one may obtain an improved estimate for p above.”
• Poincaré and Brunn-Minkowski inequalities on the boundary of weighted Riemannian manifolds (2017, methodology): “Further applications of L2-duality in the context of obtaining Poincaré-type inequalities may be found in [28, 27, 40, 33, 7, 34].”
• Brascamp–Lieb-Type Inequalities on Weighted Riemannian Manifolds with Boundary (2013, background): “We mention in passing another celebrated application of the latter duality argument in the Complex setting, namely Hörmander’s L2 estimate [13], but we refrain from attempting to generalize it here; further more recent applications may be found in [3,12,15,16,20].”