Related papers: Stochastic Growth in a Small World
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…
We investigate the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations allowing for the computation of spectral properties in the infinite-size limit and, crucially, with…
In order to characterise non-equilibrium growth processes, we study the behaviour of global quantities that depend in a non-trivial way on two different times. We discuss the dynamical scaling forms of global correlation and response…
Most agent-based models include a social network that describes the structure of interactions within the artificial population. Because of the dramatic impact of this structure on the simulated dynamics, modelers create this network for it…
For one-dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times. We argue that for self-similar growth from a single seed the…
Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…
We study the local scaling properties of driven interfaces in disordered media modeled by the Edwards-Wilkinson equation with quenched noise. We find that, due to the super-rough character of the interface close to the depinning transition,…
We study the dynamics of the Stochastic Sandpile Model on finite graphs, with two main results. First, we describe a procedure to exactly sample from the stationary distribution of the model in all connected finite graphs, extending a…
We present, as a very general method, an effective field theory to analyze models defined over small-world networks. Even if the exactness of the method is limited to the paramagnetic regions and to some special limits, it gives the exact…
We consider the problem of a subnetwork of observed nodes embedded into a larger bulk of unknown (i.e. hidden) nodes, where the aim is to infer these hidden states given information about the subnetwork dynamics. The biochemical networks…
We investigate the energy landscape of two dimensional network models for covalent glasses by means of the lid algorithm. For three different particle densities and for a range of network sizes, we exhaustively analyse many configuration…
We report on the exact treatment of a random-matrix representation of bond percolation model on a square lattice in two dimensions with occupation probability $p$. The percolation problem is mapped onto a random complex matrix composed of…
We study the connection between the highly non-convex loss function of a simple model of the fully-connected feed-forward neural network and the Hamiltonian of the spherical spin-glass model under the assumptions of: i) variable…
We determine the large size limit of a network of interacting Hawkes Processes on an adaptive network. The flipping of the node variables is taken to have an intensity given by the mean-field of the afferent edges and nodes. The flipping of…
We study a class of many body chaotic models related to the Brownian Sachdev-Ye-Kitaev model. An emergent symmetry maps the quantum dynamics into a classical stochastic process. Thus we are able to study many dynamical properties at finite…
In this work we discuss the behavior of the microcanonical temperature $\frac{\partial S(E)}{\partial E}$ obtained by means of numerical entropic sampling studies. It is observed that in almost all cases the slope of the logarithm of the…
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…
The Fermi surface anisotropy of a pseudo-gap in the spectral weight, caused by superconducting fluctuations or anti-ferromagnetic fluctuations, is calculated for a tight binding band. The importance of the Fermi surface saddle point, or hot…