Related papers: On critical points of Gaussian random fields under…
In this paper, we study the critical level-set of Gaussian free field (GFF) on the metric graph $\widetilde{\mathbb{Z}}^d,d>6$. We prove that the one-arm probability (i.e. the probability of the event that the origin is connected to the…
The main result of this paper is a bound on the distance between the distribution of an eigenfunction of the Laplacian on a compact Riemannian manifold and the Gaussian distribution. If $X$ is a random point on a manifold $M$ and $f$ is an…
A four-state clock ferromagnetic model is studied in the presence of different configurations of anisotropies and random fields. The model is considered in the limit of infinite-range interactions, for which the mean-field approach becomes…
We study the peak height distribution of certain non-stationary Gaussian random fields. The explicit peak height distribution of smooth, non-stationary Gaussian processes in 1D with general covariance is derived. The formula is determined…
We consider linear statistics of the scaled zeros of Dirichlet $L$--functions, and show that the first few moments converge to the Gaussian moments. The number of Gaussian moments depends on the particular statistic considered. The same…
This paper deals with the problem of detecting non-isotropic high-dimensional geometric structure in random graphs. Namely, we study a model of a random geometric graph in which vertices correspond to points generated randomly and…
We study numerically the region above the critical temperature of the four dimensional Random Field Ising Model. Using a cluster dynamic we measure the connected and disconnected magnetic susceptibility and the connected and disconnected…
Random fields are ubiquitous mathematical structures in physics, with applications ranging from thermodynamics and statistical physics to quantum field theory and cosmology. Recent works on information geometry of Gaussian random fields…
We discuss anisotropic scaling of long-range dependent linear random fields $X$ on ${\mathbb{Z}}^2$ with arbitrary dependence axis (direction in the plane along which the moving-average coefficients decay at a smallest rate). The scaling…
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…
The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $\mathbf{x}$ by its norm $\sqrt{\mathbf{x}^T \mathbf{x}}$. The resulting random variable…
We study random Morse functions on a Riemann manifold $(M^m,g)$ defined as a random Gaussian weighted superpositions of eigenfunctions of the Laplacian of the metric $g$. The randomness is determined by a fixed Schwartz function $w$ and a…
We determine the limit distributions of sums of deterministic chaotic variables in unimodal maps assisted by a novel renormalization group (RG) framework associated to the operation of increment of summands and rescaling. In this framework…
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…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…
Gaussian random fields are among the most important models of amorphous spatial structures and appear across length scales in a variety of physical, biological, and geological applications, from composite materials to geospatial data.…
We consider the number of edge crossings in a random graph drawing generated by projecting a random geometric graph on some compact convex set $W\subset \mathbb{R}^d$, $d\geq 3$, onto a plane. The positions of these crossings form the…
The influence of a local anisotropy of random orientation on a ferromagnetic phase transition is studied for two cases of anisotropy axis distribution. To this end a model of a random anisotropy magnet is analyzed by means of the field…
Dodson-Zeeman fuzzy topology considered as the possible mathematical framework of quantum geometric formalism. In such formalism the states of massive particle m correspond to elements of fuzzy manifold called fuzzy points. Due to their…