High Dimensional Probability IX
نویسندگان
چکیده
We explore connections between covariance representations, Bismut-type formulas and Stein's method. First, using the theory of closed symmetric forms, we derive representations for several well-known probability measures on $\mathbb{R}^d$, $d \geq 1$. When strong gradient bounds are available, these immediately lead to $L^p$-$L^q$ estimates, all $p \in (1, +\infty)$ $q = p/(p-1)$. Then, revisit $L^p$-Poincar\'e inequalities ($p 2$) standard Gaussian measure $\mathbb{R}^d$ based a representation. Moreover, nondegenerate $\alpha$-stable case, $\alpha (1,2)$, obtain pseudo-Poincar\'e inequalities, \alpha)$, via detailed analysis various at our disposal. Finally, construction kernels by forms techniques, quantitative high-dimensional CLTs in $1$-Wasserstein distance when limiting is anisotropic. The dependence parameters completely explicit rates convergence sharp.
منابع مشابه
High Dimensional Probability VI
The Circular Law for random matrices with independent log-concave rows Radosław Adamczak (University of Warsaw) I will show how the replacement principle by Tao and Vu together with Klartag’s thin shell inequality and simple bounds for the smallest singular value allow for a relatively easy proof of the circular law for the class of matrices mentioned in the title.
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Article history: Received 17 October 2014 Received in revised form 20 October 2015 Accepted 22 October 2015 Available online 10 November 2015
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ژورنال
عنوان ژورنال: Progress in probability
سال: 2023
ISSN: ['1050-6977', '2297-0428']
DOI: https://doi.org/10.1007/978-3-031-26979-0