Related papers: Zeros of smooth stationary Gaussian processes

Normalized exponential sums are entire functions of the form $$ f(z)=1+H_1e^{w_1z}+\cdots+H_ne^{w_nz}, $$ where $H_1,\ldots, H_n\in\C$ and $0<w_1<\ldots<w_n$. It is known that the zeros of such functions are in finitely many vertical strips…

We consider, for a diffusion process in R^n, the Gallavotti-Cohen functional, defined as the empirical power dissipated in a time interval by the non-conservative part of the drift. We prove a large deviation principle in the limit in which…

We establish asymptotic expansions for factorial moments of following distributions: number of cycles in a random permutation, number of inversions in a random permutation, and number of comparisons used by the randomized quick sort…

We establish asymptotic normality of weighted sums of periodograms of a stationary linear process where weights depend on the sample size. Such sums appear in numerous statistical applications and can be regarded as a discretized versions…

We consider a smooth counting function of the scaled zeros of the Riemann zeta function, around height T. We show that the first few moments tend to the Gaussian moments, with the exact number depending on the statistic considered.

We study a generic class of inelastic soft sphere models with a binary collision rate $g^\nu$ that depends on the relative velocity $g$. This includes previously studied inelastic hard spheres ($\nu=1$) and inelastic Maxwell molecules…

Assuming certain conditions on the spectral measures of centered stationary Gaussian processes on $\mathbb{R}$ (or ${\mathbb{R}}^2$), we show that the probability of the event that their zero count in an interval (resp., nodal length in a…

This thesis is concerned with the behavior of random analytic functions. In particular, we are interested in the value distribution of Taylor series with independent random coefficients. We begin with a study of the properties of Fourier…

We investigate the zero set of a stationary Gaussian process on the real line, and in particular give lower bounds for the variance of the number of points on a large interval, in all generality. We prove that this point process is never…

In this article, we study the dynamics of a nonlinear system governed by an ordinary differential equation under the combined influence of fast periodic sampling with period $\delta$ and small jump noise of size $\varepsilon, 0<…

The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…

A single joinpoint changepoint model partitions a time series into two segments, joined at the changepoint time by constraining the estimated piecewise linear regression responses to be continuous. This manuscript derives the exact…

The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy inter-sensor communication. It introduces \emph{separably estimable} observation models that generalize the…

We consider an analytic function $f$ whose zero set forms a unit intensity Poisson process on the real line. We show that repeated differentiation causes the zero set to converge in distribution to a random translate of the integers.

In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on…

In this paper we study the asymptotic behavior of a family of polynomials which are orthogonal with respect to an exponential weight on certain contours of the complex plane. The zeros of these polynomials are the nodes for complex Gaussian…

We study the asymptotic behaviour of both spherical $t$-designs and random uniform designs as the set of sampling points in non-parametric regression with spherical regressors of arbitrary dimension. We show that the corresponding…

In many applications, hypothesis testing is based on an asymptotic distribution of statistics. The aim of this paper is to clarify and extend multiple correction procedures when the statistics are asymptotically Gaussian. We propose a…

Asymptotic equivalence in Le Cam's sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression…

Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…