相关论文: Edge Effects on Local Statistics in Lattice Dimers…

Topological behavior has been observed in quantum systems including ultracold atoms. However, background harmonic traps for cold-atoms hinder direct detection of topological edge states arising at the boundary because the distortion fuses…

We consider the isochrone curves in first-passage percolation on a 2D square lattice, i.e. the boundary of the set of points which can be reached in less than a given time from a certain origin. The occurrence of an instantaneous average…

Percolation and jamming phenomena are investigated for anisotropic sequential deposition of dimers (particles occupying two adjacent adsorption sites) on a square lattice. The influence of dimer alignment on the electrical conductivity was…

We build a new perspective to count perfect matchings of a given graph. This idea is motivated by a construction on the relative cohomology group of surfaces. As an application of our theory, we reprove the celebrated Aztec Diamond theorem,…

The bulk boundary correspondence, one of the most significant features of topological matter, theoretically connects the existence of edge modes at the boundary with topological invariants of the bulk spectral bands. However, it remains…

The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we…

This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, which both are assumed to be graphs of Lipschitz continuous functions. For the deterministic case, an a priori bound explicitly dependent…

We are counting the lattice rectangles that can be constructed inside several planar shapes and identify the corresponding sequences in the OEIS.

In this exposition, we consider the dimer problem on an infinite square lattice with partially non-periodic edge weights, which we refer to as the square lattice with interface. In particular, we compute an exact integral form of the…

We consider graphs made of one-dimensional wires connected at vertices and on which may live a scalar potential. We are interested in a scattering situation where the graph is connected to infinite leads. We investigate relations between…

We consider the dimer model on the Aztec diamond with Fock's weights, which is gauge equivalent to the model with any choice of positive weight function. We prove an explicit, compact formula for the inverse Kasteleyn matrix, thus extending…

This note derives the characteristic polynomial of a graph that represents nonjump moves in a generalized game of checkers. The number of spanning trees is also determined.

At the free-fermion point, the six-vertex model with domain wall boundary conditions (DWBC) can be related to the Aztec diamond, a domino tiling problem. We study the mapping on the level of complete statistics for general domains and…

We show how to count tilings of Aztec diamonds and hexagons with defects using determinants. In several cases these determinants can be evaluated in closed form. In particular, we obtain solutions to problems 1, 2, and 10 in James Propp's…

We review the connections between the octahedral recurrence, $\lambda$-determinants and tiling problems. This provides in particular a direct combinatorial interpretation of the $\lambda$-determinant (and generalizations thereof) of an…

In critical systems, the effect of a localized perturbation affects points that are arbitrarily far from the perturbation location. In this paper, we study the effect of localized perturbations on the solution of the random dimer problem in…

We study site percolation on a square lattice with random compact diamond-shaped neighborhoods. Each site $s$ is connected to others within a neighborhood in the shape of a diamond of radius $r_s$, where $r_s$ is uniformly chosen from the…

This article has two main goals. First, it provides a self-contained exposition of the tangent plane method for the dimer model - a technique for analyzing arctic curves and limit shapes introduced by R. Kenyon and I. Prause (2020). Second,…

We develop a formalism to study the role of local defects in tight binding systems in the presence of a strong external ac electric field. It is found that the appearance and disappearance of localized states, as well as their localization…

We consider random energy landscapes constructed from d-dimensional lattices or trees. The distribution of the number of local minima in such landscapes follows a large deviation principle and we derive the associated law exactly for…