Related papers: On the linear independence of spikes and sines
The interpretation of experimental and numerical data describing off-equilibrium aging dynamics crucially depends on the connection between spontaneous and induced fluctuations. The hypothesis that linear response fluctuations are…
This paper focuses on investigating Stein's invariant shrinkage estimators for large sample covariance matrices and precision matrices in high-dimensional settings. We consider models that have nearly arbitrary population covariance…
Spectra derived from fast Fourier transform (FFT) analysis of time-domain data intrinsically contain statistical fluctuations whose distribution depends on the number of accumulated spectra contributing to a measurement. The tail of this…
Exposition of the relation between quasi-independent and Sidon sets, theorems of Pisier according to the method of Bourgain
We study the capacity with which a system of independent neuron-like units represents a given set of stimuli. We assume that each neuron provides a fixed amount of information, and that the information provided by different neurons has a…
Spikes are the currency in central nervous systems for information transmission and processing. They are also believed to play an essential role in low-power consumption of the biological systems, whose efficiency attracts increasing…
The aim of this paper, triggered by some discussions in the astrophysics community raised by astro-ph/0508529, is to introduce the issue of `fits' from a probabilistic perspective (also known as Bayesian), with special attention to the…
We introduce a random matrix model where the entries are dependent across both rows and columns. More precisely, we investigate matrices of the form $\X=(X_{(i-1)n+t})_{it}\in\R^{p\times n}$ derived from a linear process $X_t=\sum_j c_j…
We investigate the fluctuations of linear spectral statistics of a Wigner matrix $W\_N$ deformed by a deterministic diagonal perturbation $D\_N$, around a deterministic equivalent which can be expressed in terms of the free convolution…
We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically independent diagonals. Along the diagonals the entries may be…
Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic…
The aim of this paper is to show how free probability theory sheds light on spectral properties of deformed matricial models and provides a unified understanding of various asymptotic phenomena such as spectral measure description,…
Process of the nonlinear deformation of the surface wave in shallow water is studied. Main attention is paid to the relation between the Fourier-spectrum and wave steepness. It is shown that the spectral harmonics of the initially sine wave…
Ultrahigh-dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research. Among others, Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] propose an…
Given any two rational numbers $r_1$ and $r_2$, a necessary and sufficient condition is established for the three numbers $1$, $\cos (\pi r_1)$, and $\cos (\pi r_2)$ to be rationally independent. Extending a classical fact sometimes…
Neuronal dynamics is intrinsically unstable, producing activity fluctuations that are essentially scale-free. Here we show that while these scale-free fluctuations are independent of temporal input statistics, they can be entrained by input…
We prove limit theorems for the number of fixed points, descents, and inversions of iterated random-to-top shuffles in two asymptotic regimes. Our proofs are analytic, and they utilize new combinatorial decompositions that represent each…
The present paper introduces a modified version of cyclic-monotone independence which originally arose in the context of random matrices, and also introduces its natural analogy called cyclic-Boolean independence. We investigate formulas…
We study optimal approximation of stochastic processes by polynomial splines with free knots. The number of free knots is either a priori fixed or may depend on the particular trajectory. For the $s$-fold integrated Wiener process as well…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…