Results 1 to 10 of about 108,474 (123)
Small ball probabilities for linear images of high dimensional distributions [PDF]
International Mathematics Research Notices, 2014 We study concentration properties of random vectors of the form $AX$, where $X = (X_1, ..., X_n)$ has independent coordinates and $A$ is a given matrix. We show that the distribution of $AX$ is well spread in space whenever the distributions of $X_i$ are
Rudelson, Mark, Vershynin, Roman
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Asymptotics of Karhunen–Loève Eigenvalues for Sub-Fractional Brownian Motion and Its Application
Fractal and Fractional, 2021 In the present paper, the Karhunen–Loève eigenvalues for a sub-fractional Brownian motion are considered. Rigorous large n asymptotics for those eigenvalues are shown, based on the functional analysis method.
Chun-Hao Cai, Jun-Qi Hu, Ying-Li Wang
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Quantitative invertibility of random matrices: a combinatorial perspective
Discrete Analysis, 2021 Quantitative invertibility of random matrices: a combinatorial perspective, Discrete Analysis 2021:10, 38 pp. This paper concerns the general and much studied question of how likely a large random real or complex square matrix is to be invertible, and ...
Vishesh Jain
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Phase Retrieval Without Small-Ball Probability Assumptions [PDF]
IEEE Transactions on Information Theory, 2018 15 pages; v3: to appear in IEEE Trans. Info. Theory; v2: minor revisions and clarifications; presented in part at the 2015 SampTA Conference, see http://doi.org/10.1109/SAMPTA.2015.7148923 and http://doi.org/10.1109/SAMPTA.2015 ...
Felix Krahmer, Yi-Kai Liu
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Small ball probabilities for stable convolutions [PDF]
ESAIM: Probability and Statistics, 2007 Summary: We investigate the small deviations under various norms for stable processes defined by the convolution of a smooth function \(f : \; ]0, +\infty[ \;\to \mathbb{R} \) with a real \(S\alpha S\) Lévy process. We show that the small ball exponent is uniquely determined by the norm and by the behaviour of \(f\) at zero, which extends the results ...
Aurzada, Frank, Simon, Thomas
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Small Ball Probability, Inverse Theorems, and Applications [PDF]
, 2013 Let $ $ be a real random variable with mean zero and variance one and $A={a_1,...,a_n}$ be a multi-set in $\R^d$. The random sum $$S_A := a_1 _1 + ... + a_n _n $$ where $ _i$ are iid copies of $ $ is of fundamental importance in probability and its applications.
Nguyen, Hoi H., Vu, Van H.
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Small ball probability and Dvoretzky’s Theorem
Israel Journal of Mathematics, 2007 Large deviation estimates are by now a standard tool inthe Asymptotic Convex Geometry, contrary to small deviationresults. In this note we present a novel application of a smalldeviations inequality to a problem related to the diameters of random sections of high dimensional convex bodies.
Klartag, Bo'az, Vershynin, Roman
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Small ball probability estimates in terms of width [PDF]
Studia Mathematica, 2005 10 ...
Latała, Rafał, Oleszkiewicz, Krzysztof
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Hitting spheres on hyperbolic spaces [PDF]
, 2011 For a hyperbolic Brownian motion on the Poincar\'e half-plane $\mathbb{H}^2$, starting from a point of hyperbolic coordinates $z=(\eta, \alpha)$ inside a hyperbolic disc $U$ of radius $\bar{\eta}$, we obtain the probability of hitting the boundary ...
E. Orsingher +3 more
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Low Diameter Graph Decompositions by Approximate Distance Computation [PDF]
, 2019 In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the probability that ...
Becker, Ruben +2 more
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