Related papers: Local Statistics of Realizable Vertex Models
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
We establish several properties of the integrated density of states for random quantum graphs: Under appropriate ergodicity and amenability assumptions, the integrated density of states can be defined using an exhaustion procedure by…
An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that account for an approximation of a folding arc. The numerical…
We study the dimer model for a planar bipartite graph N embedded in a disk, with boundary vertices on the boundary of the disk. Counting dimer configurations with specified boundary conditions gives a point in the totally nonnegative…
We collect a number of striking recent results in a study of dimers on infinite regular bipartite lattices and also on regular bipartite graphs. We clearly separate rigorously proven results from conjectures. A primary goal is to show…
In this article, we study the question of the statistical convergence of the 1-dimensional Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal estimator of the Reeb graph, which gives, as a byproduct, a…
We propose a generic framework to describe classical Ising-like models defined on arbitrary graphs. The energy spectrum is shown to be the Hadamard transform of a suitably defined sparse "coding" vector associated with the graph. We expect…
This thesis deals with applications of experimental mathematics to a number of problems. The first problem is related to random graph statistics. We consider a certain class of Galton-Watson random trees and look at the total height…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
In this paper we analyse both the dynamics and the high density physics of the infinite dimensional lattice gas model for random heteropolymers recently introduced in \cite{jort}. Restricting ourselves to site-disordered heteropolymers, we…
The problem of maximising the number of cliques among $n$-vertex graphs from various graph classes has received considerable attention. We investigate this problem for the class of $1$-planar graphs where we determine precisely the maximum…
We show that it is possible to determine the locus of Fisher zeroes in the thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs and their dual quadrangulations by matching up the real part of the high- and…
In this work, we study a class of nonlocal-in-time kinetic models of incompressible dilute polymeric fluids. The system couples a macroscopic balance of linear momentum equation with a mezoscopic subdiffusive Fokker-Planck equation…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We study the Potts model on locally tree-like random graphs of arbitrary degree distribution. Using a population dynamics algorithm we numerically solve the problem exactly. We confirm our results with simulations. Comparisons with a…
Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…
A visibility representation is a classical drawing style of planar graphs. It displays the vertices of a graph as horizontal vertex-segments, and each edge is represented by a vertical edge-segment touching the segments of its end vertices;…
In order to apply quantum topology methods to nonplanar graphs, we define a planar diagram category that describes the local topology of embeddings of graphs into surfaces. These \emph{virtual graphs} are a categorical interpretation of…
A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some…