相关论文: Solution of the Voter Model by Spectral Analysis

We consider the voter model with $M$ states initially in the system. Using generating functions, we pose the spectral problem for the Markov transition matrix and solve for all eigenvalues and eigenvectors exactly. With this solution, we…

We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean field equations for the degree distribution and its generating function are given. The exact solution of these equations for…

The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph.…

In this study, we analyzed urn models by solving the discrete-time master equation using an expansion in moments. This approach is a viable alternative to conventional methods, such as system-size expansion, allowing for the determination…

The voter model is a classical interacting particle system, modelling how global consensus is formed by local imitation. We analyse the time to consensus for a particular family of voter models when the underlying structure is a scale-free…

While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…

An example of full solution of the inverse scattering problem on the half line is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a…

This paper introduces a new method to estimate the spectral distribution of a population covariance matrix from high-dimensional data. The method is founded on a meaningful generalization of the seminal Marcenko-Pastur equation, originally…

Problems of consensus in multi-agent systems are often viewed as a series of independent, simultaneous local decisions made between a limited set of options, all aimed at reaching a global agreement. Key challenges in these protocols…

The spectral expansion of the Green's tensor for a planar multilayered structure allows us to semi analytically obtain the angular spectrum representation of the field scattered by an arbitrary dielectric perturbation present in the…

We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…

Numerous vector angular spectrum methods have been presented to model the vectorial nature of diffractive electromagnetic field, facilitating optical field engineering in polarization-related and high numerical aperture systems. However,…

Markov chain Monte Carlo is widely used in a variety of scientific applications to generate approximate samples from intractable distributions. A thorough understanding of the convergence and mixing properties of these Markov chains can be…

The Neighborhood Attack model is a Voter type model, which takes a finite graph, assigns 1's and -1's to its nodes (vertices), and then runs a Markov chain on the graph by uniformly at random picking a node at every turn, and then switching…

For more than a decade, graphs have been used to model the voting behavior taking place in parliaments. However, the methods described in the literature suffer from several limitations. The two main ones are that 1) they rely on some…

Recently we showed that a simple model of network rewiring could be solved exactly for any time and any parameter value. We also showed that this model can be recast in terms of several well known models of statistical physics such as Urn…

This paper considers the problem of estimating the population spectral distribution from a sample covariance matrix in large dimensional situations. We generalize the contour-integral based method in Mestre (2008) and present a local moment…

A mixed semiclassical initial value representation expression for spectroscopic calculations is derived. The formulation takes advantage of the time-averaging filtering and the hierarchical properties of different trajectory based…

We investigate the consensus dynamics of the voter model on large random graphs with heterogeneous and directed features, focusing in particular on networks with power-law degree distributions. By extending recent results on sparse directed…

This work addresses a central challenge in the numerical analysis of the cutoff spatially homogeneous Boltzmann equation: the development of rigorously justified, accurate numerical schemes. We present (i) a novel Fourier spectral method…