Related papers: Local Statistics of Realizable Vertex Models

The velocity fluctuations for point vortex models are studied for the {\alpha}-turbulence equations, which are characterized by a fractional Laplacian relation between active scalar and the streamfunction. In particular, we focus on the…

We develop a diagrammatic approach with local and nonlocal self-energy diagrams, constructed from the local irreducible vertex. This approach includes the local correlations of dynamical mean field theory and long-range correlations beyond.…

We study random surfaces which arise as height functions of random perfect matchings (a.k.a. dimer configurations) on an weighted, bipartite, doubly periodic graph G embedded in the plane. We derive explicit formulas for the surface tension…

This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…

There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable minor-closed class, such as the class of all planar graphs. Here we use combinatorial and probabilistic methods to investigate a…

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…

Building upon the theory of graph limits and the Aldous-Hoover representation and inspired by Panchenko's work on asymptotic Gibbs measures (Annals of Probability 2013), we construct continuous embeddings of discrete probability…

In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…

We present the first parallel fixed-parameter algorithm for subgraph isomorphism in planar graphs, bounded-genus graphs, and, more generally, all minor-closed graphs of locally bounded treewidth. Our randomized low depth algorithm has a…

We present a geometrical approach for studying dimers. We introduce a connection for dimer problems on bipartite and non-bipartite graphs. In the bipartite case the connection is flat but has non-trivial ${\bf Z}_2$ holonomy round certain…

We give an example of a relation between local and effective properties for elastic structures, up to geometric constants. The model considered is a periodic structure with isotropic and homogeneous local elasticity tensor in planar linear…

We show how to compute the probability of any given local configuration in a random tiling of the plane with dominos. That is, we explicitly compute the measures of cylinder sets for the measure of maximal entropy $\mu$ on the space of…

Temporal graphs are graphs whose edges are labelled with times at which they are active. Their time-sensitivity provides a useful model of real networks, but renders many problems studied on temporal graphs more computationally complex than…

We prove a general multi-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers…

We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings,…

We solve a 4-(bond)-vertex model on an ensemble of 3-regular Phi3 planar random graphs, which has the effect of coupling the vertex model to 2D quantum gravity. The method of solution, by mapping onto an Ising model in field, is inspired by…

Dyadic lattice graphs and their duals are commonly used as discrete approximations to the hyperbolic plane. We use them to give examples of random rooted graphs that are stationary for simple random walk, but whose duals have only a…

The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…

The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…

In this paper, we revisit self-similar solutions of the two-dimensional stationary incompressible Navier-Stokes equations under scaling symmetries, also known as Jeffery-Hamel solutions. We investigate the local patterns of smooth…