Related papers: Extremes of Gaussian Random Fields with maximum va…

Let M be a compact smooth manifold of dimension n with or without boundary, and f : M $\rightarrow$ R be a smooth Gaussian random field. It is very natural to suppose that for a large positive real u, the random excursion set {f $\ge$ u} is…

In this paper we provide an upper bound for the conjunction probability of independent Gaussian smooth processes and then we prove that this bound is a good approximation with exponentially smaller error. Our result confirms the heuristic…

We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of random matrices that includes the normalized adjacency matrices of the Erd\H{o}s-R\'enyi graph $G(N,p)$. Tracy-Widom fluctuations of the extreme…

We investigate the relationship between ergodicity and asymptotic Gaussianity of isotropic spherical random fields, in the high-resolution (or high-frequency) limit. In particular, our results suggest that under a wide variety of…

This is the second of two papers devoted to the proof of conformal invariance of the critical double random current on the square lattice. More precisely, we show convergence of loop ensembles obtained by taking the cluster boundaries in…

In this article we give a general criterion for some dependent Gaussian models to belong to maximal domain of attraction of Gumbel, following an application of the Stein-Chen method studied in Arratia et al(1989). We also show the…

Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…

We consider the Gaussian free field $\varphi$ on $\mathbb{Z}^2$ at large spatial scales $N$ and give sharp bounds on the probability $\theta(a,N)$ that the radius of a finite cluster in the excursion set $\{\varphi \geq a\}$ on the…

We obtain sharp sufficient conditions for exponentially integrable stochastic processes $X=\{X(t)\!\!: t\in [0,1]\}$, to have sample paths with bounded $\Phi$-variation. When $X$ is moreover Gaussian, we also provide a bound of the…

Likelihood inference for max-stable random fields is in general impossible because their finite-dimen\-sional probability density functions are unknown or cannot be computed efficiently. The weighted composite likelihood approach that…

Cohen, Guyon, Perrin and Pontier have given assumptions under which the second-order quadratic variations of a Gaussian process converge almost surely to a deterministic limit. In this paper we present two new convergence results about…

Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…

We consider the extremal properties of the highly flexible univariate extended skew-normal distribution. We derive the well-known Mills' inequalities and Mills' ratio for the extended skew-normal distribution and establish the asymptotic…

In a previous paper, the authors introduced an approach to prove that the statistics of the extremes of a log-correlated Gaussian field converge to a Poisson-Dirichlet variable at the level of the Gibbs measure at low temperature and under…

We consider a Gaussian field $X = \{X_t, t \in T\}$ with values in a Banach space $B$ defined on a parametric set $T$ equal to $R^m$ or $Z^m.$ It is supposed that the distribution $\cal P$ of $X_t$ is independent of $t.$ We consider the…

We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated to the probability that the process remains below a…

Consider a branching random walk $(G_u)_{u\in \mathbb T}$ on the general linear group $\textrm{GL}(V)$ of a finite dimensional space $V$, where $\mathbb T$ is the associated genealogical tree with nodes $u$. For any starting point $v \in V…

In this paper we define (empirical) quadratic variations for a Gaussian isotropic random field $f$ on a unit sphere as sums over equidistant increments on one single geodesic line on the surface of the sphere. We prove a noncentral limit…

We develop a primal bootstrap framework for effective field theories in the presence of a graviton pole, based on finite-resolution sampling rather than smearing, while also allowing direct control over the number of subtractions. We show…

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…