Related papers: Large deviations for zeros of $P(\phi)_2$ random p…

Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…

We consider random trigonometric polynomials with general dependent coefficients. We show that under mild hypotheses on the structure of dependence, the asymptotics as the degree goes to infinity of the expected number of real zeros…

We consider an asymmetric zero range process in infinite volume with zero mean and random jump rates starting from equilibrium. We investigate the large deviations from the hydrodynamical limit of the empirical distribution of particles and…

We investigate the high-dimensional asymptotic distributional behavior of the $\mathbf{f}$-vector of a random Vietoris-Rips complex, that is generated over a stationary Poisson point process in $[-\frac{1}{2}, \frac{1}{2}]^d$ as the space…

We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a…

There is a result of Diaconis and Freedman which says that, in a limiting sense, for large collections of high-dimensional data most one-dimensional projections of the data are approximately Gaussian. This paper gives quantitative versions…

We consider a diffusion equation in $\mathbb{R}^d$ with drift equal to the gradient of a homogeneous potential of degree $1+\gamma$, with $0<\gamma<1$, and local variance equal to $\varepsilon^2$ with $\varepsilon\to 0$. The associated…

We investigate small deviation properties of Gaussian random fields in the space $L_q(\R^N,\mu)$ where $\mu$ is an arbitrary finite compactly supported Borel measure. Of special interest are hereby "thin" measures $\mu$, i.e., those which…

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 give asymptotic approximations of the zeros of certain high degree polynomials. The zeros can be used to compute the filter coefficients in the dilation equations which define the compactly supported orthogonal Daubechies wavelets.…

We investigate the distribution of critical points of certain isotropic random functions $\Phi$ on $\mathbb{R}^m$. We show that the distribution of critical points of $\Phi(Rx)$, suitably normalized, converge a.s. and $L^2$ as random…

Let $\{\varphi_k\}_{k=0}^\infty $ be a sequence of orthonormal polynomials on the unit circle (OPUC) with respect to a probability measure $ \mu $. We study the variance of the number of zeros of random linear combinations of the form $$…

We consider random trigonometric polynomials of the form \[ f_n(t):=\frac{1}{\sqrt{n}} \sum_{k=1}^{n}a_k \cos(k t)+b_k \sin(k t), \] where $(a_k)_{k\geq 1}$ and $(b_k)_{k\geq 1}$ are two independent stationary Gaussian processes with the…

We study large deviations for measurable averaging operators on state spaces of dynamical systems. Our main motivation is the Hecke operators on the modular curve Y_0(p^n) and their generalization to higher rank S-arithmetic quotients. We…

For random polynomials with i.i.d. (independent and identically distribu-ted) zeros following any common probability distribution $\mu$ with support contained in the unit circle, the empirical measures of the zeros of their first and higher…

Consider the zero set of the random power series f(z)=sum a_n z^n with i.i.d. complex Gaussian coefficients a_n. We show that these zeros form a determinantal process: more precisely, their joint intensity can be written as a minor of the…

We present a large deviation principle at speed N for the largest eigenvalue of some additively deformed Wigner matrices. In particular this includes Gaussian ensembles with full-rank general deformation. For the non-Gaussian ensembles, the…

We establish large deviations properties valid for almost every sample path of a class of stationary mixing processes $(X_1,..., X_n,...)$. These properties are inherited from those of $S_n=\sum_{i=1}^nX_i$ and describe how the local…

In this note, we prove a central limit theorem for smooth linear statistics of zeros of random polynomials which are linear combinations of orthogonal polynomials with iid standard complex Gaussian coefficients. Along the way, we obtain…