Small ball probability estimates for log-concave measures
By Grigoris Paouris. 2012
125 citations recorded by the source corpus.
We establish a small ball probability inequality for isotropic log-concave probability measures: there exist absolute constants c1, c2 > 0 such that if X is an isotropic log-concave random vector in R with ψ2 constant bounded by b and if A is a non-zero n × n matrix, then for every e ∈ (0, c1) and y ∈ R, P (‖Ax− y‖2 6 e‖A‖HS) 6 e ( c2 b ‖A‖HS ‖A‖op )2 , where c1, c2 > 0 are absolute constants.
Subfields: Applied Mathematics, Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/75dcaa957f892c3d6547af94f03337574323eb3e
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In Applied Mathematics
- Olivier Guédon
- Emanuel Milman
- N. Dafnis
- Grigoris Paouris
- Bo'az Klartag
- Yuansi Chen
- A. V. Kolesnikov
- Radosław Adamczak
In Artificial Intelligence
In Statistics and Probability
Citations in the corpus
- Interpolating Thin-Shell and Sharp Large-Deviation Estimates for Lsotropic Log-Concave Measures (2010, background): “This leads to the following scale-invariant definition of η as η := ‖A‖2HS /(b(2)α ‖A‖ 2 op), which naturally also appears in the work of Paouris [34, 35].”
- Centroid Bodies and the Logarithmic Laplace Transform - A Unified Approach (2011, unknown): “t the origin, then I2(µ)2 = trace Cov(µ). In [25], Paouris defines q∗(µ) as follows: q∗(µ) := sup{q∈ N;k∗(Zq(µ)) ≥ q} . It is straightforward to check that all of Paouris’ results involving q∗(µ) from [25, 26] remain valid when replacing it with q∗ c(µ) when c>0 is a fixed universal constant, where”
- Small Ball Probabilities for Linear Images of High-Dimensional Distributions (2014, unknown): “1”
- Small ball probability estimates, ψ2-behavior and the hyperplane conjecture (2010, methodology): “2U[n] q c(; )’ n (see Proposition 4.8 in [ 23 ]).”