Results 1 to 10 of about 381,656 (263)

Phase Retrieval Without Small-Ball Probability Assumptions [PDF]

IEEE Transactions on Information Theory, 2017
In the context of the phase retrieval problem, it is known that certain natural classes of measurements, such as Fourier measurements and random Bernoulli measurements, do not lead to the unique reconstruction of all possible signals, even in combination
Krahmer, Felix, Liu, Yi-Kai
core   +3 more sources

Small ball probability, Inverse theorems, and applications [PDF]

, 2012
Let $\xi$ 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 $$S_A := a_1 \xi_1 + ... + a_n \xi_n $$ where $\xi_i$ are iid copies of $\xi$ is of fundamental importance in probability
A. A. Sherstov, A. Edelman, A. Kolmogorov, A. Kolmogorov, A. Pajor, A. Sali, A. Sali, A. Sárközy, A. T. Bharucha-Reid, B. A. Rogozin, C. Bordenave, C. G. Esséen, D. A. Spielman, D. A. Spielman, D. Hilbert, D. Kleitman, D. Kleitman, D. Kleitman, D. S. Gunderson, E. Szemerédi, E. Viola, F. Götze, G. Freiman, G. Halász, G. Katona, H. Goldstine, H. Nguyen, H. Nguyen, H. Nguyen, J. Bourgain, J. E. Littlewood, J. Griggs, J. Kahn, J. Komlós, J. Komlós, K. Costello, M. Rudelson, M. Rudelson, M. Rudelson, M. Rudelson, O. Friedland, P. Erdős, P. Erdős, P. Frankl, R. A. Proctor, R. Stanley, S. Muroga, S. Muroga, T. Tao, T. Tao, T. Tao, T. Tao, T. Tao, T. Tao, T. Tao, T. Tao, T. Tao, T. Tao, T. Tao   +58 more
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Small ball probability and Dvoretzky theorem

Israel Journal of Mathematics, 2004
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 ...
Klartag, Bo'az, Vershynin, Roman
core   +4 more sources

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
core   +6 more sources

Small ball probability for the condition number of random matrices [PDF]

, 2019
Let $A$ be an $n\times n$ random matrix with i.i.d. entries of zero mean, unit variance and a bounded subgaussian moment. We show that the condition number $s_{\max}(A)/s_{\min}(A)$ satisfies the small ball probability estimate $${\mathbb P}\big\{s_{\max}
DA Spielman, K Tatarko, M Rudelson, R Vershynin   +3 more
core   +2 more sources

Optimal quantization of probabilities concentrated on small balls [PDF]

Forum Mathematicum, 2008
We consider probability distributions which are uniformly distributed on a disjoint union of balls with equal radius. For small enough radius the optimal quantization error is calculated explicitly in terms of the ball centroids.
Kreitmeier, Wolfgang
core   +4 more sources

Asymptotic Properties of the Semi-Parametric Estimators of the Conditional Density for Functional Data in the Single Index Model with Missing Data at Random

Statistica, 2022
The main objective of this work is to estimate, semi-parametrically, the mode of a conditional density when the response is a real valued random variable subject to censored phenomenon and the predictor takes values in a semi-metric space. We assume that
Abbes Rabhi, Nadia Kadiri, Sanaà Dounya Mekki   +2 more
doaj   +1 more source

Kolmogorov Entropy for Convergence Rate in Incomplete Functional Time Series: Application to Percentile and Cumulative Estimation in High Dimensional Data

Entropy, 2023
The convergence rate for free-distribution functional data analyses is challenging. It requires some advanced pure mathematics functional analysis tools.
Ouahiba Litimein, Fatimah Alshahrani, Salim Bouzebda, Ali Laksaci, Boubaker Mechab   +4 more
doaj   +1 more source

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
openaire   +2 more sources

Analytic Combinatorics of the Mabinogion Urn [PDF]

Discrete Mathematics & Theoretical Computer Science, 2008
The Mabinogion urn is a simple model of the spread of influences amongst versatile populations. It corresponds to a non-standard urn with balls of two colours: each time a ball is drawn, it causes a ball of the other kind to switch its colour.
Philippe Flajolet, Thierry Huillet
doaj   +1 more source