Related papers: Harmonic pinnacles in the Discrete Gaussian model

We study microscopic observables of the Discrete Gaussian model (i.e., the Gaussian free field restricted to take integer values) at high temperature using the renormalisation group method. In particular, we show the central limit theorem…

We consider a model of a two-dimensional interface of the SOS type, with finite-range, even, strictly convex, twice continuously differentiable interactions. We prove that, under an arbitrarily weak potential favouring zero-height, the…

The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions, at sufficiently high temperature, we show that the scaling limit of the infinite-volume gradient Gibbs state with zero mean…

The Discrete Gaussian Chain is a model of interfaces $\Psi : \mathbf{Z} \to \mathbf{Z}$ governed by the Hamiltonian $$ H(\Psi)= \sum_{i\neq j} J_\alpha(|i-j|) |\Psi_i -\Psi_j|^2 $$ with long-range coupling constants $J_\alpha(k)\asymp…

We prove that if $(\mathcal{M},d)$ is an $n$-point metric space that embeds quasisymmetrically into a Hilbert space, then for every $\tau>0$ there is a random subset $\mathcal{Z}$ of $\mathcal{M}$ such that for any pair of points $x,y\in…

We use the holographic approach to compare the Hall viscosity $\eta_H$ and the angular momentum density ${\cal J}$ in gapless systems in $2+1$ dimensions at finite temperature. We start with a conformal fixed point and turn on a…

The dimer model on a planar bipartite graph can be viewed as a random surface measure. We study these fluctuations for a dimer model on the square grid with two different classes of weights and provide a condition for their equivalence. In…

Maxima of the linear density field form a point process that can be used to understand the spatial distribution of virialized halos that collapsed from initially overdense regions. However, owing to the peak constraint, clustering…

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…

Higher-spin vertices containing up to quintic interactions at the Lagrangian level are explicitly calculated in the one-form sector of the non-linear unfolded higher-spin equations using a $\beta\to-\infty$--shifted contracting homotopy…

For a given pseudo-Hermitian Hamiltonian of the standard form: H=p^2/2m+v(x), we reduce the problem of finding the most general (pseudo-)metric operator \eta satisfying H^\dagger=\eta H \eta^{-1} to the solution of a differential equation.…

We give a polynomial-time algorithm to sample from the Gibbs measure of the Sherrington-Kirkpatrick model with negligible total-variation distance (TVD) error up to inverse temperature $\beta < 1/2$. Prior work obtained TVD error guarantees…

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre $\beta$ ensemble, characterised by the Dyson parameter $\beta$, and the Laguerre…

In this paper, we introduce the stationary harmonic measure in the upper half plane. By bounding this measure, we are able to define both the discrete and continuous time diffusion limit aggregation (DLA) in the upper half plane with…

Many low temperature disordered systems are expected to exhibit Poisson-Dirichlet (PD) statistics. In this paper, we focus on the case when the underlying disorder is a logarithmically correlated Gaussian process $\phi_N$ on the box…

Let $V = \{ v_1,\dots,v_N\}$ be a collection of $N$ vectors that live near a discrete sphere. We consider discrete directional maximal functions on $\mathbb{Z}^2$ where the set of directions lies in $V$, given by \[ \sup_{v \in V, k \geq C…

We discuss the results of extensive numerical simulations in order to estimate the scaling exponents associated with kinetic roughening in higher dimensions, up to d=7+1. To this end, we study the restricted solid - on - solid growth model,…

We study elliptic gradient systems with fractional laplacian operators on the whole space $$ (- \Delta)^\mathbf s \mathbf u =\nabla H (\mathbf u) \ \ \text{in}\ \ \mathbf{R}^n,$$ where $\mathbf u:\mathbf{R}^n\to \mathbf{R}^m$, $H\in…

We analyze several Galerkin approximations of a Gaussian random field $\mathcal{Z}\colon\mathcal{D}\times\Omega\to\mathbb{R}$ indexed by a Euclidean domain $\mathcal{D}\subset\mathbb{R}^d$ whose covariance structure is determined by a…

We consider a robust linear regression model $y=X\beta^* + \eta$, where an adversary oblivious to the design $X\in \mathbb{R}^{n\times d}$ may choose $\eta$ to corrupt all but an $\alpha$ fraction of the observations $y$ in an arbitrary…