Related papers: Limit shapes and harmonic tricks
We construct a one-parameter family of lattice models starting from a two-dimensional rational conformal field theory on a torus with a regular lattice of holes, each of which is equipped with a conformal boundary condition. The lattice…
In this paper, we study the asymptotic behaviour of plane partitions distributed according to a $q^{\text{Volume}}$-weighted Muttalib--Borodin ensemble and its associated discrete point process. We establish a Large Deviation Principle for…
The model problem of a plane angle for a second-order elliptic system subject to Dirichlet, mixed, and Neumann boundary conditions is analyzed. For each boundary condition, the existence of solutions of the form $r^\lambda v$ is reduced to…
We present new computations of approximately length-minimizing polygons with fixed thickness. These curves model the centerlines of "tight" knotted tubes with minimal length and fixed circular cross-section. Our curves approximately…
We study the partition function of both Close-Packed Dimers and the Critical Ising Model on a square lattice embedded on a genus two surface. Using numerical and analytical methods we show that the determinants of the Kasteleyn adjacency…
In this article we study the double dimer model on hyperbolic Temperleyan graphs via circle packings. We prove that on such graphs, the weak limit of the dimer model exists if and only if the removed black vertex from the boundary of the…
In this tutorial, we pedagogically review recent developments in the field of non-interacting fermionic phases of matter, focussing on the low energy description of higher-order topological insulators in terms of the Dirac equation. Our aim…
In this work, some classical results of the pfaffian theory of the dimer model based on the work of Kasteleyn, Fisher and Temperley are introduced in a fermionic framework. Then we shall detail the bosonic formulation of the model {\it via}…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
Analytic expressions that describe Casimir interactions over the entire range of separations have been limited to planar surfaces. Here we derive analytic expressions for the classical or high-temperature limit of Casimir interactions…
Twin-width is a structural width parameter introduced by Bonnet, Kim, Thomass\'e and Watrigant [FOCS 2020], and has interesting applications in the areas of logic on graphs and in parameterized algorithmics. Very briefly, the essence of…
We present medial parametrization, a new approach to parameterizing any compact planar domain bounded by simple closed curves. The basic premise behind our proposed approach is to use two close Voronoi sites, which we call dipoles, to…
In 2004, Muzereau et al. showed how to use a reduction algorithm of the discrete logarithm problem to Diffie-Hellman problem in order to estimate lower bound on Diffie-Hellman problem on elliptic curves. They presented their estimates for…
In Arakelov theory a completion of an arithmetic surface is achieved by enlarging the group of divisors by formal linear combinations of the ``closed fibers at infinity''. Manin described the dual graph of any such closed fiber in terms of…
We consider the $q^\text{Volume}$ lozenge tiling model on a large, finite hexagon. It is well-known that random lozenge tilings of the hexagon correspond to a two-dimensional determinantal point process via a bijection with ensembles of…
We study several numerical discretization techniques for the one-space plus one-time dimensional Dirac equation, including finite difference and space-time finite element methods. Two finite difference schemes and several space-time finite…
We give new examples of manifolds that appear as cross sections of tangent cones of non-collapsed Ricci limit spaces. It was shown by Colding-Naber that the homeomorphism types of the tangent cones of a fixed point of such a space do not…
We explore the connections between the well-studied Aztec Diamond graphs and a new family of graphs called the Half-Hexagons, discovered by Jonathan Novak. In particular, both families of graphs have very simple domino shuffling algorithms,…
We obtain scaling and local limit results for large random Young tableaux of fixed shape $\lambda^0$ via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). More precisely, we prove: (1) an explicit…
The convex hull peeling of a point set consists in taking the convex hull, then removing the extreme points and iterating that procedure until no point remains. The boundary of each hull is called a layer. Following on from [15], we study…