Related papers: Extreme values for two-dimensional discrete Gaussi…

We study the distribution of the maximum of a large class of Gaussian fields indexed by a box $V_N\subset Z^d$ and possessing logarithmic correlations up to local defects that are sufficiently rare. Under appropriate assumptions that…

We study the local structure of the extremal process associated with the Discrete Gaussian Free Field (DGFF) in scaled-up (square-)lattice versions of bounded open planar domains subject to mild regularity conditions on the boundary. We…

We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we…

We consider discrete Gaussian free fields with ergodic random conductances on a class of random subgraphs of $\mathbb{Z}^{d}$, $d \geq 2$, including i.i.d.\ supercritical percolation clusters, where the conductances are possibly unbounded…

We study the one-arm probability in the level-set percolation of the discrete and metric-graph Gaussian free field (GFF) defined on a box with Dirichlet boundary conditions. For the metric-graph case, we establish asymptotic estimates on…

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…

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…

This work aims to extend the existing results on thick points of logarithmic-correlated Gaussian Free Fields to Gaussian random fields that are more singular. To be specific, we adopt a sphere averaging regularization to study…

Consider a rowwise independent triangular array of gamma random variables with varying parameters. Under several different conditions on the shape parameter, we show that the sequence of row-maximums converges weakly after linear or power…

The explicit formulae for the height distribution and expected number of local maxima have been obtained for isotropic Gaussian random fields on certain low-dimensional Euclidean space or low-dimensional spheres.

We study the extremal process associated with the Discrete Gaussian Free Field on the square lattice and elucidate how the conformal symmetries manifest themselves in the scaling limit. Specifically, we prove that the joint process of…

We consider a class of non-homogeneous, continuous, centered Gaussian random fields $\{X_h(t), t \in {\cal M}_h;\,0 < h \le 1\}$ where ${\cal M}_h$ denotes a rescaled smooth manifold, i.e. ${\cal M}_h = \frac{1}{h} {\cal M},$ and study the…

Let $X(s,t), (s,t)\in E$, with $E\subset \mathbb{R}^2$ a compact set, be a centered two dimensional Gaussian random field with continuous trajectories and variance function $\sigma(s,t)$. Denote by $\mathcal{L}=\{(s,t):…

We prove two theorems concerning extreme values of general Gaussian fields. Our first theorem concerns with the concept of multiple peaks. A theorem of Chatterjee states that when a centered Gaussian field admits the so-called…

We consider fluctuations in the distribution of critical points - saddle points, minima and maxima - of random gaussian fields. We calculate the asymptotic limits of the two point correlation function for various critical point densities,…

We have obtained some upper bounds for the probability distribution of extremes of a self-similar Gaussian random field with stationary rectangular increments that are defined on the compact spaces. The probability distributions of extremes…

Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…

We consider the Gumbel or extreme value statistics describing the distribution function p_G(x_max) of the maximum values of a random field x within patches of fixed size. We present, for smooth Gaussian random fields in two and three…

We define and study the Dirichlet fractional Gaussian fields on the Sierpinski gasket and show that they are limits of fractional discrete Gaussian fields defined on the sequence of canonical approximating graphs.

In this paper, we study a random field constructed from the two-dimensional Gaussian free field (GFF) by modifying the variance along the scales in the neighborhood of each point. The construction can be seen as a local martingale transform…