Related papers: Multiple Points of Gaussian Random Fields
The fixed-point analysis refers to the study of fixed-points that arise in the context of complex systems with many interacting entities. In this expository paper, we describe four levels of fixed-points in mean-field interacting particle…
We study the behaviour of the point process of critical points of isotropic stationary Gaussian fields. We compute the main term in the asymptotic expansion of the two-point correlation function near the diagonal. Our main result implies…
We study the energy landscape of a model of a single particle on a random potential, that is, we investigate the topology of level sets of smooth random fields on $\mathbb R^{N}$ of the form $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a…
We prove that the second moment of the number of critical points of any sufficiently regular random field, for example with almost surely $ C^3 $ sample paths, defined over a compact Whitney stratified manifold is finite. Our results hold…
Random fields in nature often have, to a good approximation, Gaussian characteristics. For such fields, the relative densities of umbilical points -- topological defects which can be classified into three types -- have certain fixed values.…
Massive and massless Gaussian free fields can be described as generalized Gaussian processes indexed by an appropriate space of functions. In this article we study various approaches to approximate these fields and look at the fractal…
We study deviation probabilities for the number of high positioned particles in branching Brownian motion, and confirm a conjecture of Derrida and Shi (2016). We also solve the corresponding problem for the two-dimensional discrete Gaussian…
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…
We determine the asymptotic law for the fluctuations of the total number of critical points of random Gaussian spherical harmonics in the high degree limit. Our results have implications on the sophistication degree of an appropriate…
The problem of characterization of Gibbs random fields is considered. Various Gibbsianness criteria are obtained using the earlier developed one-point framework which in particular allows to describe random fields by means of either…
We establish thresholds for the feasibility of random multi-graph alignment in two models. In the Gaussian model, we demonstrate an "all-or-nothing" phenomenon: above a critical threshold, exact alignment is achievable with high…
We deal with the existence of three distinct solutions for a poly-Laplacian system with a parameter on finite graphs and a $(p,q)$-Laplacian system with a parameter on locally finite graphs.The main tool is an abstract critical points…
We prove a central limit theorem concerning the number of critical points in large cubes of an isotropic Gaussian random function on a Euclidean space.
We obtain sufficient conditions of stochastic equivalence of Gaussian random fields with special covariance function. These results generalize Doob's transformation (condition of stochastic equivalence of a Gaussian and a Wiener processes)…
In this paper, we show that the methods of mathematical statistical physics can be successfully applied to random fields in finite volumes. As a result, we obtain simple necessary and sufficient conditions for the existence and uniqueness…
We prove that under fairly general conditions properly rescaled determinantal random point field converges to a generalized Gaussian random process.
Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…
In this paper, we present a novel approach to investigate the existence of multiple critical points for a class of nonsmooth functionals. This method provides a robust framework to analyze the existence of solutions for problems involving…
The nature of level set percolation in the two-dimension Gaussian Free Field has been an elusive question. Using a loop-model mapping, we show that there is a nontrivial percolation transition, and characterize the critical point. In…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…