Related papers: Sojourns of Vector-Valued Stationary Gaussian Rand…

Consider an affine Gaussian field X : R 2 $\rightarrow$ R, that is a process equal in law to Z(At), where Z is isotropic and A : R2 $\rightarrow$ R2 is a self-adjoint definite positive matrix. Denote 0 < $\lambda$ = $\lambda$\_2 /…

We study the landscape complexity of the Hamiltonian $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a smooth Gaussian process with isotropic increments on $\mathbb R^{N}$. This model describes a single particle on a random potential in…

In large dimension, we study the asymptotic behavior of the mean number of critical points with index k below a level u for an isotropic centered Gaussian random field defined on a family of subsets of $R^d$ depending on d. We prove the…

In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…

We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…

Let $f:\mathbb{R}^d \to \mathbb{R}^k$ be a smooth centered stationary Gaussian field and $\mathcal{B} \subset \mathbb{R}^d$ be a bounded Borel set. In this paper, we determine the asymptotics as $R \to \infty$ of all the cumulants of the…

Let $\Gamma_{g}$ be the fundamental group of a closed connected orientable surface of genus $g\geq2$. We develop a new method for integrating over the representation space $\mathbb{X}_{g,n}=\mathrm{Hom}(\Gamma_{g},S_{n})$ where $S_{n}$ is…

The present work investigates two properties of level crossings of a stationary Gaussian process $X(t)$ with autocorrelation function $R_X(\tau)$. We show firstly that if $R_X(\tau)$ admits finite second and fourth derivatives at the…

We develop techniques for determining the exact asymptotic speed of convergence in the multidimensional normal approximation of smooth functions of Gaussian fields. As a by-product, our findings yield exact limits and often give rise to…

In this paper we consider elliptical random vectors X in R^d,d>1 with stochastic representation A R U where R is a positive random radius independent of the random vector U which is uniformly distributed on the unit sphere of R^d and A is a…

A previous paper by the authors found explicit contour integral formulas for certain joint moments of the multi-species q-TAZRP (totally asymmetric zero range process), using algebraic methods. These contour integral formulas have a…

In this paper, we study Kaplan-Meier V- and U-statistics respectively defined as $\theta(\widehat{F}_n)=\sum_{i,j}K(X_{[i:n]},X_{[j:n]})W_iW_j$ and $\theta_U(\widehat{F}_n)=\sum_{i\neq j}K(X_{[i:n]},X_{[j:n]})W_iW_j/\sum_{i\neq j}W_iW_j$,…

Let $X_H(t), t\ge 0$ be a fractional Brownian motion with Hurst index $H\in(0,1}$ and define a gamma-reflected process $W_\Ga(t)=X_H(t)-ct-\gammainf_{s\in[0,t]}\left(X_H(s)-cs \right)$, $t\ge0$ with $c>0,\gamma \in [0,1]$ two given…

This paper addresses the issue of estimating the expectation of a real-valued random variable of the form $X = g(\mathbf{U})$ where $g$ is a deterministic function and $\mathbf{U}$ can be a random finite- or infinite-dimensional vector.…

We study the behavior of high-dimensional robust regression estimators in the asymptotic regime where $p/n$ tends to a finite non-zero limit. More specifically, we study ridge-regularized estimators, i.e…

Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive…

In this paper, we consider the extreme behavior of a Gaussian random field $f(t)$ living on a compact set $T$. In particular, we are interested in tail events associated with the integral $\int_Te^{f(t)}\,dt$. We construct a (non-Gaussian)…

This paper considers extreme values attained by a centered, multidimensional Gaussian process $X(t)= (X_1(t),\ldots,X_n(t))$ minus drift $d(t)=(d_1(t),\ldots,d_n(t))$, on an arbitrary set $T$. Under mild regularity conditions, we establish…

Gaussian random processes which variances reach theirs maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of theirs trajectories have been evaluated using Double Sum Method…

The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…