Related papers: Statistical mechanics on isoradial graphs
Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…
We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…
A Random Graph is a random object which take its values in the space of graphs. We take advantage of the expressibility of graphs in order to model the uncertainty about the existence of causal relationships within a given set of variables.…
Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…
Driven-dissipative many-body systems are difficult to analyze analytically due to their non-equilibrium dynamics, dissipation and many-body interactions. In this paper, we consider a driven-dissipative infinite-range Ising model with local…
It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the…
Causal Models are like Dependency Graphs and Belief Nets in that they provide a structure and a set of assumptions from which a joint distribution can, in principle, be computed. Unlike Dependency Graphs, Causal Models are models of…
We consider several models whose motivation arises from statistical mechanics. We begin by investigating some families of distributions of translation invariant subgraphs of some Cayley graphs, and in particular subgraphs of the square…
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…
We extend the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that…
We introduce orbital graphs and discuss some of their basic properties. Then we focus on their usefulness for search algorithms for permutation groups, including finding the intersection of groups and the stabilizer of sets in a group.
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…
A family of multispecies Ising models on generalized regular random graphs is investigated in the thermodynamic limit. The architecture is specified by class-dependent couplings and magnetic fields. We prove that the magnetizations,…
We describe, in an intrinsic way and using the global chart provided by Ito's parallel transport, a generalisation of the notion of geodesic (as critical path of an energy functional) to diffusion processes on Riemannian manifolds. These…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A…
We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…