Related papers: Gaussian fields and percolation
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an…
We establish a sprinkled decoupling inequality for increasing events of Gaussian vectors with an error that depends only on the maximum pairwise correlation. As an application we prove the non-triviality of the percolation phase transition…
Percolation models describe the inside of a porous material. The theory emerged timidly in the middle of the twentieth century before becoming one of the major objects of interest in probability and mathematical physics. The golden age of…
We study the motion of smooth, strictly convex bodies in $\mathbb{R}^n$ expanding in the direction of their normal vector field with speed depending on Gauss curvature and support function.
We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…
Scalar fields describe interesting phenomena such as Higgs bosons, dark matter and dark energy, and are found to be quite common in physical theories. These fields are susceptible to gravitational forces so that being massless is not enough…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
For $d \geq 3$ we obtain an approximation of the zero-average Gaussian free field on the discrete $d$-dimensional torus of large side length $N$ by the Gaussian free field on $\mathbb Z^d$, valid in boxes of roughly side length $N -…
In this short survey of the applications of wide-field, multi-object spectroscopy to galaxy evolution, large-scale structure and cosmology, I interleave summaries of the general goals and state of play in these fields with specific examples…
Random advection of Lagrangian tracer scalar field $\theta (t,x)$ by a one-dimensional, spatially smooth and short-correlated in time velocity field is considered. Scalar fluctuations are maintained by a source concentrated at the integral…
Road networks are characterised by several structural and geometric properties. Their topological structure determines partially its hierarchical arrangement, but since these are networks that are spatially situated and, therefore,…
The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters size distributions is developed. It allows for full description of percolation transition…
A study and numerical modeling of the cosmological evolution of a classical scalar field with the Higgs potential was carried out. Based on the formulated similarity properties of cosmological models, their main characteristics are studied…
There has been considerable recent progress in discovering and understanding quantum phases and fluctuations produced by strong correlations. Heavy fermion systems are an ideal platform for systematic studies because low and competing…
We review main features and problems of higher spin field theory and flash some ways along which it has been developed over last decades.
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
Shape information is of great importance in many applications. For example, the oil-bearing capacity of sand bodies, the subterranean remnants of ancient rivers, is related to their cross-sectional shapes. The analysis of these shapes is…