相关论文: Low Correlation Noise Stability of Symmetric Sets

Weak lensing experiments are a powerful probe of cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant…

The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…

We prove a vector-valued inequality for the Gaussian noise stability (i.e. we prove a vector-valued Borell inequality) for Euclidean functions taking values in the two-dimensional sphere, for all correlation parameters at most $1/10$ in…

Under standard assumptions including stationary and serially uncorrelated Gaussian gravitational wave stochastic background signal and noise distributions, as well as homogenous detector sensitivities, the standard cross-correlation…

Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…

This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…

Many geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given noisy measurements of a subset of their pairwise relative transforms. This problem is…

This paper studies the functional uniqueness and stability of Gaussian priors in optimal $L^1$ estimation. While it is well known that the Gaussian prior uniquely induces linear conditional means under Gaussian noise, the analogous question…

We consider symmetric two-user Gaussian interference channel with common messages. We derive an upper bound on the sum capacity, and show that the upper bound is tight in the low interference regime, where the optimal transmission scheme is…

The symbol error rate of the minimum distance detector for an arbitrary multi-dimensional constellation impaired by additive white Gaussian noise is characterized as the product of a completely monotone function with a non-negative power of…

We consider the estimation of an n-dimensional vector s from the noisy element-wise measurements of $\mathbf{s}\mathbf{s}^T$, a generic problem that arises in statistics and machine learning. We study a mismatched Bayesian inference…

We study the sensitivity to noise of |permanent(X)|^2 for random real and complex n x n Gaussian matrices X, and show that asymptotically the correlation between the noisy and noiseless outcomes tends to zero when the noise level is…

For the problem of nonparametric detection of signal in Gaussian white noise we point out strong asymptotically minimax tests. The sets of alternatives are a ball in Besov space $B^r_{2\infty}$ with "small" balls in $L_2$ removed.

In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian)…

We investigate the top of the spectrum of discrete Anderson Hamiltonians with correlated Gaussian noise in the large volume limit. The class of Gaussian noises under consideration allows for long-range correlations. We show that the largest…

We study an isoperimetric problem described by a functional that consists of the standard Gaussian perimeter and the norm of the barycenter. This second term has a repulsive effect, and it is in competition with the perimeter. Because of…

The density deconvolution problem involves recovering a target density g from a sample that has been corrupted by noise. From the perspective of Le Cam's local asymptotic normality theory, we show that non-parametric density deconvolution…

We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit…

Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…

Noisy network coding, which elegantly combines the conventional compress-and-forward relaying strategy and ideas from network coding, has recently drawn much attention for its simplicity and optimality in achieving to within constant gap of…