Related papers: Maximum of sparsely equicorrelated Gaussian fields…
Experimental configuration for investigating the dynamics and the statistics of the phase locking level of coupled lasers that have no common frequency is presented. The results reveal that the probability distribution of the phase locking…
Consider the point process (in $\mathbb{R}^d$) of local maxima of smooth Gaussian fields, with sufficient decay of correlation at infinity, above a level $u$. We show that this point process, rescaled appropriately, converges weakly to a…
In this paper we provide a new geometric characterization of the Hirschfeld-Gebelein-R\'{e}nyi maximal correlation of a pair of random $(X,Y)$, as well as of the chordal slope of the nontrivial boundary of the hypercontractivity ribbon of…
We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and…
We consider the thick points of random walk, i.e. points where the local time is a fraction of the maximum. In two dimensions, we answer a question of Dembo, Peres, Rosen and Zeitouni and compute the number of thick points of planar random…
Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices,…
We compute exact asymptotic results for the probability of the occurrence of large deviations of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we…
A finite-support constraint on the parameter space is used to derive a lower bound on the error of an estimator of the correlation coefficient in the bivariate exponential distribution. The bound is then exploited to examine optimality of…
The well-known "Janson's inequality" gives Poisson-like upper bounds for the lower tail probability \Pr(X \le (1-\eps)\E X) when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations,…
The $r$-parallel set of a measurable set $A \subseteq \mathbb R^d$ is the set of all points whose distance from $A$ is at most $r$. In this paper, we show that the surface area of an $r$-parallel set in $\mathbb R^d$ with volume at most $V$…
Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…
We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are…
We study the extreme point process associated to the off-diagonal components in the matrix representation of the Gaussian $\beta$-Ensemble and prove its convergence to Poisson point process as $n\to +\infty$ when the inverse temperature…
Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
Our problem is to find a good approximation to the P-value of the maximum of a random field of test statistics for a cone alternative at each point in a sample of Gaussian random fields. These test statistics have been proposed in the…
We derive a Gaussian approximation result for the maximum of a sum of random vectors under $(2+\iota)$-th moments. Our main theorem is abstract and nonasymptotic, and can be applied to a variety of statistical learning problems. The proof…
We consider the extreme value statistics of $N$ independent and identically distributed random variables, which is a classic problem in probability theory. When $N\to\infty$, fluctuations around the maximum of the variables are described by…
We consider the extremal shot noise defined by $$M(y)=\sup\{mh(y-x);(x,m)\in\Phi\},$$ where $\Phi$ is a Poisson point process on $\bbR^d\times (0,+\infty)$ with intensity $\lambda dxG(dm)$ and $h:\bbR^d\to [0,+\infty]$ is a measurable…
The seminal papers of Pickands [1,2] paved the way for a systematic study of high exceedance probabilities of both stationary and non-stationary Gaussian processes. Yet, in the vector-valued setting, due to the lack of key tools including…