Related papers: Random lattice triangulations: Structure and algor…
We analyse the numbers of closed paths of length $k\in\mathbb{N}$ on two important regular lattices: the hexagonal lattice (also called $\textit{graphene}$ in chemistry) and its dual triangular lattice. These numbers form a moment sequence…
The geometry of optical lattices can be engineered allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question readily accessible to atomic systems is related…
Rotation Averaging is a non-convex optimization problem that determines orientations of a collection of cameras from their images of a 3D scene. The problem has been studied using a variety of distances and robustifiers. The intrinsic (or…
Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical…
We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by…
We study pinball billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls are non-elastic: the outgoing angle with the normal vector to the boundary is a uniform factor $\lambda < 1$ smaller than the…
We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are…
Dissipative dynamical systems characterised by two basins of attraction are found in many physical systems, notably in hydrodynamics where laminar and turbulent regimes can coexist. The state space of such systems is structured around a…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
Roughening transitions are often characterized by unusual scaling properties. As an example we investigate the roughening transition in a solid-on-solid growth process with edge evaporation [Phys. Rev. Lett. 76, 2746 (1996)], where the…
We study a randomized quadrature algorithm to approximate the integral of periodic functions defined over the high-dimensional unit cube. Recent work by Kritzer, Kuo, Nuyens and Ullrich (2019) shows that rank-1 lattice rules with a randomly…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
Entanglement entropy is a powerful tool to detect continuous, discontinuous and even topological phase transitions in quantum as well as classical systems. In this work, von Neumann and Renyi entanglement entropies are studied numerically…
The hard core model in statistical physics is a probability distribution on independent sets in a graph in which the weight of any independent set I is proportional to lambda^(|I|), where lambda > 0 is the vertex activity. We show that…
We define the correlation of holes on the triangular lattice under periodic boundary conditions and study its asymptotics as the distances between the holes grow to infinity. We prove that the joint correlation of an arbitrary collection of…
We introduce and investigate numerically a minimal class of dynamical triangulations of two-dimensional gravity on the sphere in which only vertices of order five, six or seven are permitted. We show firstly that this restriction of the…
We study random plane partitions with respect to volume measures with periodic weights of arbitrarily high period. We show that near the vertical boundary the system develops up to as many turning points as the period of the weights, and…
Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…
The Longest Edge Bisection of a triangle is performed by joining the midpoint of its longest edge to the opposite vertex. Applying this procedure iteratively produces an infinite family of triangles. Surprisingly, a classical result of…
We explore a roughening phase transition that occurs in the entanglement dynamics of certain quantum circuits. Viewing entanglement as the free energy of a membrane in a circuit-defined random environment, there is a competition between…