We study when a sub‐Gaussian matrix can become a near isometry on a set, show that previous best‐known dependence on the sub‐Gaussian norm was suboptimal, and present the optimal dependence. Our result not only answers a remaining question posed by Liaw, Mehrabian, Plan, and Vershynin ...
Exponential bounds for the distribution of the norm of subgaussian random vectors Exponential bounds for the distribution of norms of sub-Gaussian random vectors taking its values in R n are found. The random vector X taking its values in R n is called sub-Gaussian with respect to a symmetric...
e. concentration of the Euclidean norm of the linear image of a random vector and ... F Gtze,H Sambale,A Sinulis - 《Electronic Journal of Probability》 被引量: 0发表: 2021年 加载更多 来源期刊 Electronic Communications in Probability 2013/06/12 研究点推荐 sub-gaussian random variables ...
Adaptive widths of the approximation functional on the Sobolev space W[supr][sub2] with Gaussian measure.Determines the tight orders for the Kolmogorov and adaptive widths of the Sobolev spaces equipped with a Gaussian measure in the L[sub 1]-norm and L[sub infinity]-norm. Use of ...
Exact value for subgaussian norm of centered indicator random variableMathematics - ProbabilityEugene OstrovskyLeonid SirotaarXivOstrovsky E., Sirota L. Exact value for subgaussian norm of centered in- dicator random variable. arXiv:1405.6749v1 [math.PR] 26 May 2014...
Secondly, we obtain a sharp estimate for the optimal lower and upper bounds of norm distortion rates of Gaussian random matrices under a given erasure ratio. This allows us to establish the strong restricted isometry property with the almost optimal RIP constants, which plays a central role in ...
For a random variable $\xi$ let $au_{\varphi_p}(\xi)$ denote $\inf\{c\ge 0 :\; \forall_{\lambda\in\mathbb{R}}\; \ln\mathbb{E}\exp(\lambda\xi)\le\varphi_p(c\lambda)\}$; $au_{\varphi_p}$ is a norm in a space $Sub_{\varphi_p}(\Omega) =\{\xi: \; au_{\...
Looks at the distribution estimate of the norm of sub-Gaussian random processes in space Lp (T). These estimates are also considered. For more general spaces, namely the spaces Sub 蠁 (惟) such estimates can also be found. These estimates are used to find the rate of convergence of sub-...
The obtained result allows to estimate the distribution of deviation of a sub-Gaussian random process from some measurable function in the norm of Lp() and in the norm of Orlicz space. The paper generalizes results of [Theory Probab. Math. Statist. 58 (1999), 51鈥 66] for the norm of ...
This paper investigates an upper bound of the operator norm for sub-Gaussian tailed random matrices. A lot of attention has been put on uniformly bounded sub-Gaussian tailed random matrices with independent coefficients. However, little has been done for sub-Gaussian tailed random matrices whose ...