Related papers: Limit shapes for the dimer model

We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain new numerical results on the Erd\H{o}s problem of finding…

Local existence properties of initial boundary value problems associated with a new type of systems of differential equations with "maxima" are investigated.

We use the recently developed method of weighted dependency graphs to prove central limit theorems for the number of occurrences of any fixed pattern in multiset permutations and in set partitions. This generalizes results for patterns of…

We consider the directed polymer model in the weak disorder phase under the assumption that the partition function is $L^p$-bounded for some $p>1+\frac{2}d$. We prove that the point-to-point partition function can be approximated by two…

We study limit shapes in two equivalent models: the six-vertex model in the $c\to0$ limit and the random Mallows permutation with restricted permutation matrix. We give the Euler-Lagrange equation for the limit shape and show how to solve…

We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a typical tiling of an arbitrary finite region can…

For planar polynomials systems the existence of an invariant algebraic curve limits the number of limit cycles not contained in this curve. We present a general approach to prove non existence of periodic orbits not contained in this given…

Sharp bounds are given for solutions to the minimal surface equation with vanishing boundary values over domains containing sectors of opening bigger than pi.

We study the properties of the quantum states in the one-dimensional system with a shifted periodic potential in both the discrete model and the continuous model. With open boundary conditions, the edge states appear in the energy gaps…

Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with five parameters is…

We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar or embedded on the torus. The set of positive face weights…

We prove the local convergence of uniform bipartite maps with prescribed face degrees in the high genus regime. Unlike in the previous work arxiv:2012.05813 on the subject, we do not make any assumption on the tail of the face degrees,…

We study models for a directed polymer in a random environment (DPRE) in which the polymer traverses a hierarchical diamond graph and the random environment is defined through random variables attached to the vertices. For these models, we…

We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…

We consider ergodic translation-invariant Gibbs measures for the dimer model (i.e. perfect matchings) on the hexagonal lattice. The complement to a dimer configuration is a fully-packed loop configuration: each vertex has degree two. This…

Magnetic bound states are a general phenomenon in low dimensional antiferromagnets with gapped singlet states. Using Raman scattering on three compounds as dedicated examples we show how exchange topology, dimensionality, defects and…

Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by…

We study the symmetry properties of limit profiles of nonautonomous nonlinear parabolic systems with Dirichlet boundary conditions in radial bounded domains. In the case of competitive systems, we show that if the initial profiles satisfy a…

We prove an analog of Levinson's theorem for scattering on a weighted (m+1)-vertex graph with a semi-infinite path attached to one of its vertices. In particular, we show that the number of bound states in such a scattering problem is equal…

Using topological circles in the Freudenthal compactification of a graph as infinite cycles, we extend to locally finite graphs a result of Oberly and Sumner on the Hamiltonicity of finite graphs. This answers a question of Stein, and gives…