Related papers: Temperleyan Domino Tilings with Holes
We study a system of 1D noninteracting spinless fermions in a confining trap at finite temperature. We first derive a useful and general relation for the fluctuations of the occupation numbers valid for arbitrary confining trap, as well as…
The six-vertex model is an important toy-model in statistical mechanics for two-dimensional ice with a natural parameter $\Delta$. When $\Delta = 0$, the so-called free-fermion point, the model is in natural correspondence with domino…
We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector…
We carry out the asymptotic analysis of repulsive ensembles of N particles which are discrete analogues of continuous 1d log-gases or beta-ensembles of random matrix theory. The ensembles that we study have several groups of particles which…
We introduce a pairing on local intersection cohomology groups of variations of pure Hodge structure, which we call the asymptotic height pairing. Our original application of this pairing was to answer a question on the Ceresa cycle posed…
We study fluctuations in the number of zeros of random analytic functions given by a Taylor series whose coefficients are independent complex Gaussians. When the functions are entire, we find sharp bounds for the asymptotic growth rate of…
The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, $u_t=J*u-u:=Lu$, in an exterior domain, $\Omega$, which excludes one or several holes, and with zero Dirichlet data on…
We analyse the statistical distribution function for the height fluctuations of brittle fracture surfaces using extensive experimental data sampled on widely different materials and geometries. We compare a direct measurement of the…
We revisit the homogenization problem for the Poisson equation in periodically perforated domains with zero Neumann data at the boundary of the holes and prescribed Dirichlet data at the outer boundary. It is known that, if the periodicity…
Discrete Hamiltonian variational integrators are derived from Type II and Type III generating functions for symplectic maps, and in this paper we establish a variational error analysis result that relates the order of accuracy of 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…
By random complex zeroes we mean the zero set of a random entire function whose Taylor coefficients are independent complex-valued Gaussian variables, and the variance of the k-th coefficient is 1/k!. This zero set is distribution invariant…
We say that a function $f \in L^1(\mathbb{R})$ tiles at level $w$ by a discrete translation set $\Lambda \subset \mathbb{R}$, if we have $\sum_{\lambda \in \Lambda} f(x-\lambda)=w$ a.e. In this paper we survey the main results, and prove…
We discuss asymptotic properties of a family of discrete probability measures which may be used to model particle configurations with a wall on a set of discrete nodes. The correlations are shown to be determinantal and are expressed in…
Stochastic growth models in the Kardar-Parisi-Zhang (KPZ) universality class exhibit remarkable fluctuation phenomena. While a variety of powerful methods have led to a detailed understanding of their typical fluctuations or large…
The enumeration of lozenge tilings of hexagons with holes has been studied intensively in recent years. Researchers tried to find shapes and positions of holes in hexagonal regions so that the number of lozenge tilings of the resulting…
String theory and ``quantum geometry'' have recently offered independent statistical mechanical explanations of black hole thermodynamics. But these successes raise a new problem: why should models with such different microscopic degrees of…
We treat random rank-$D$ tensor models as $D$-dimensional quantum field theories---tensor field theories (TFT)---and review some of their non-perturbative methods. We classify the correlation functions of complex tensor field theories by…
Under certain reality conditions, a general solution to the dispersionless Toda lattice hierarchy describes deformations of simply-connected plane domains with a smooth boundary. The solution depends on an arbitrary (real positive) function…
The emergent nature of spacetime geometry and black holes can be directly probed in simple holographic duals of higher spin gravity and tensionless string theory. To this end, we study time dependent thermal correlation functions of gauge…