相关论文: Excursion decomposition of the 2D continuum GFF

We show that the construction of a random continuum $\mathcal{C}$ from independent two-sided Brownian motions as considered in arXiv:2004.01367 almost surely yields a non-degenerate indecomposable but not-hereditary indecomposable…

We consider the function $f(g)$ that assigns to an orientable surface $M$ of genus $g$ the maximal number of free commuting independent involutions on $M$. We show that the surface of minimal genus $g$ with $f(g)=n$ is a real moment-angle…

Let $F$ be a homogeneous form of degree $d$ in $n$ variables. A Waring decomposition of $F$ is a way to express $F$ as a sum of $d^{th}$ powers of linear forms. In this paper we consider the decompositions of a form as a sum of expressions,…

We show that the Gelfand character $ \chi_G$ of a finite group $G $ (i.e. the sum of all irreducible complex characters of $G$ ) may be realized as a `` twisted trace'' $ g \mapsto Tr( \rho_g \circ T) $ for a suitable involutive linear…

We identify a natural analytic continuation in four dimensions from Minkowski signature to a signature with two time-like momentum components. For two, three and four-point diagrams at fixed external momenta, this continuation can be…

In this paper we consider the problem of constructing graph Fourier transforms (GFTs) for directed graphs (digraphs), with a focus on developing multiple GFT designs that can capture different types of variation over the digraph…

We describe two classes of Gaussian self-similar random fields: with strictly stationary rectangular increments and with mild stationary rectangular increments. We find explicit spectral and moving average representations for the fields…

Gravitational form factors (GFFs), defined through the matrix elements of the energy-momentum tensor, provide critical insights into the internal structure of nucleons and nuclei. In particular, their Fourier transforms -- evaluated in the…

The activation gap $\Delta$ of the fractional quantum Hall states at constant fillings $\nu =2/3$ and 2/5 has been measured as a function of the perpendicular magnetic field $B$. A linear dependence of $\Delta$ on $B$ is observed while…

Transport properties of 2D materials especially close to their boundary has received much attention after the successful fabrication of graphene and other fascinating materials afterwards. While most previous work is devoted to the…

We analyze pole skipping of stress tensor two-point functions in two-dimensional quantum field theories perturbed away from conformality by a relevant deformation. The retarded two-point Green's function can be formally computed in…

This paper focuses on various decompositions of topological measures, deficient topological measures, signed topological measures, and signed deficient topological measures. These set functions generalize measures and correspond to certain…

The study of the Ornstein--Zernike decay of subcritical two-point functions in equilibrium statistical mechanics has a history going back over a century. Despite this, the crossover from Ornstein--Zernike decay to critical power-law decay…

We study the level-set percolation of the Gaussian free field on Z^d, d bigger or equal to 3. We consider a level alpha such that the excursion-set of the Gaussian free field above alpha percolates. We derive large deviation estimates on…

We investigate a special case of infinite urn schemes first considered by Karlin (1967), especially its occupancy and odd-occupancy processes. We first propose a natural randomization of these two processes and their decompositions. We then…

Random field excursions is an increasingly vital topic within data analysis in medicine, cosmology, materials science, etc. This work is the first detailed study of their Betti numbers in the so-called `sparse' regime. Specifically, we…

We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$-flat chain admits a decomposition in set-indecomposable sub-chains. This generalizes the decomposition of sets of finite…

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited…

We revisit the geometrical meaning of statistical isotropy that is manifest in excursion sets of smooth random fields in two dimensions. Using the contour Minkowski tensor, $\W_1$, as our basic tool we first examine geometrical properties…

We consider representations of tensors as sums of decomposable tensors or, equivalently, decomposition of multilinear forms into one--forms. In this short note we show that there exists a particular finite strongly orthogonal decomposition…