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In this article, we revisit the question of fluctuations of linear statistics of beta ensembles in the single cut and non-critical regime for general potentials $V$ under mild regularity and growth assumptions. Our main objective is to…

We address the dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the atmospheric boundary layer with a stable temperature stratification in mind. Traditional approaches to…

We prove a local central limit theorem for fluctuations of linear statistics of smooth enough test functions under the canonical Gibbs measure of two-dimensional Coulomb gases at any positive temperature. The proof relies on the existing…

In geometry processing, smoothness energies are commonly used to model scattered data interpolation, dense data denoising, and regularization during shape optimization. The squared Laplacian energy is a popular choice of energy and has a…

We investigate equal spheres packings generated from several experiments and from a large number of different numerical simulations. The structural organization of these disordered packings is studied in terms of the network of common…

It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…

We study the stress distribution profiles and the height and thickness fluctuations of lipid membranes in the tilted gel state by Monte Carlo simulations of a generic coarse-grained model for lipid membranes, which reproduces many known…

Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit $d$-dimensional sphere ($d\ge 2$). We study the convergence in Total Variation distance for their nonlinear statistics in the high energy limit, i.e., for…

Simple random coverage models, well studied in Euclidean space, can also be defined on a general compact metric space. By analogy with the geometric models, and with the discrete coupon collector's problem and with cover times for finite…

We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…

We study the statistics of single particle Lagrangian velocity in a shell model of turbulence. We show that the small scale velocity fluctuations are intermittent, with scaling exponents connected to the Eulerian structure function scaling…

Consider the classical $(2+1)$-dimensional Solid-On-Solid model above a hard wall on an $L\times L$ box of $\bbZ^2$. The model describes a crystal surface by assigning a non-negative integer height $\eta_x$ to each site $x$ in the box and 0…

We study the defect (or "signed area") distribution of toral Laplace eigenfunctions restricted to shrinking balls of radius above the Planck scale, in either random Gaussian scenario ("Arithmetic Random Waves"), or deterministic…

We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic…

Let $S$ be a punctured Riemann surface with Euler characteristic $\chi(S)<0$. For any unitary representation $\rho: \pi_1(S) \to U(N)$, we introduce its renormalized energy and its harmonic representatives, which are equivariant harmonic…

We investigate equilibrium configurations for surface energies which contain the squared $L^2$ norm of the difference of the mean curvature H and the spontaneous curvature $c_o$ coupled with the elastic energy of the boundary curve, which…

We prove a central limit theorem for smooth linear statistics related to the zero divisors of Gaussian i.i.d. centered holomorphic sections of tensor powers of a Hermitian holomorphic line bundle over a non-compact Hermitian manifold.

Spatial random permutations were originally studied due to their connections to Bose-Einstein condensation, but they possess many interesting properties of their own. For random permutations of a regular lattice with periodic boundary…

The inertial subrange of turbulent scales is commonly reflected by a power law signature in ensemble statistics such as the energy spectrum and structure functions - both in theory and from observations. Despite promising findings on the…

We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…