Related papers: Delocalization of two-dimensional random surfaces …
Let $0<\alpha<1$. We obtain the boundedness of the discrete fractional Hardy-Littlewood maximal operators ${\mathcal M}_\alpha$ on discrete weighted Lebesgue spaces. From this and a discrete version of Whitney decomposition theorem, we…
In continuing the study of harmonic mapping from 2-dimensional Riemannian simplicial complexes in order to construct minimal surfaces with singularity, we obtain an a-priori regularity result concerning the real analyticity of the free…
We study properties of stable, strictly stable and locally outermost marginally outer trapped surfaces in spacelike hypersurfaces of spacetimes possessing certain symmetries such as isometries, homotheties and conformal Killings. We first…
Inspired by the study of edge statistics of random band matrices, we investigate random walks on large $d$-dimensional periodic lattices, whose transition matrices are determined by discretized density functions. Under certain moment…
We consider random Gaussian eigenfunctions of the Laplacian on the standard torus, and investigate the number of nodal intersections against a line segment. The expected intersection number, against any smooth curve, is universally…
The main goal of this article is to understand how the length spectrum of a random surface depends on its genus. Here a random surface means a surface obtained by randomly gluing together an even number of triangles carrying a fixed metric.…
On any spacelike surface in a lightcone of four dimensional Lorentz-Minkowski space a distinguished smooth function is considered. It is shown how both extrinsic and intrinsic geometry of such a surface is codified by this function. The…
We study automorphisms of smooth hypersurfaces in projective space $\mathbb{P}^{n+1}$ whose fixed loci have codimension at most two for $n\geq2$. While classifications of possible orders of automorphisms are known, our aim is to explore the…
A homomorphism height function on the $d$-dimensional torus $\mathbb{Z}_n^d$ is a function taking integer values on the vertices of the torus with consecutive integers assigned to adjacent vertices. A Lipschitz height function is defined…
Previous experimental and numerical studies showed that two-dimensional roughness elements can stabilize disturbances inside a hypersonic boundary layer, and eventually delay the transition onset. The objective of this paper is to evaluate…
We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative…
Solving the Plateau problem means to find the surface with minimal area among all surfaces with a given boundary. Part of the problem actually consists of giving a suitable definition to the notions of 'surface', 'area' and 'boundary'. In…
For a family of bond percolation models on Z^{2} that includes the Fortuin-Kasteleyn random cluster model, we consider properties of the ``droplet'' that results, in the percolating regime, from conditioning on the existence of an open dual…
We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…
We study large random dissections of polygons. We consider random dissections of a regular polygon with $n$ sides, which are chosen according to Boltzmann weights in the domain of attraction of a stable law of index $\theta\in(1,2]$. As $n$…
The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…
Using the Wang-Landau flat histogram Monte Carlo (FHMC) simulation technique, we were able to study two types of triangulated spherical surface models in which the two-dimensional extrinsic curvature energy is assumed in the Hamiltonian.…
We report results of lattice Boltzmann simulations of a high-speed drainage of liquid films squeezed between a smooth sphere and a randomly rough plane. A significant decrease in the hydrodynamic resistance force as compared with that…
The influence of a strong surface potential on the critical depinning of an elastic system driven in a random medium is considered. If the surface potential prevents depinning completely the elastic system shows a parabolic displacement…
We study a new notion of critical point for the area of surfaces under the Legendrian constraint, called parametrized Hamiltonian stationary Legendrian varifolds (PHSLVs). We establish several fundamental properties of these objects,…