相关论文: Fixation for Two-Dimensional $\mathcal U$-ISING an…
The influence of zealots on the noisy voter model is studied theoretically and numerically at the mean-field level. The noisy voter model is a modification of the voter model that includes a second mechanism for transitions between states:…
We consider the transcendental entire function $ f(z)=z+e^{-z} $, which has a doubly parabolic Baker domain $U$ of degree two, i.e. an invariant stable component for which all iterates converge locally uniformly to infity, and for which the…
The stability of a discrete time crystal against thermal fluctuations has been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert equation of a periodically-driven classical system composed of interacting spins, each of…
Evolutionary game theory provides a mathematical foundation for cross-disciplinary fertilization, especially for integrating ideas from artificial intelligence and game theory. Such integration offers a transparent and rigorous approach to…
Given a transition matrix $P$ indexed by a finite set $V$ of vertices, the voter model is a discrete-time Markov chain in $\{0,1\}^V$ where at each time-step a randomly chosen vertex $x$ imitates the opinion of vertex $y$ with probability…
A one-dimensional interacting particle system is said to exhibit interface tightness if starting in an initial condition describing the interface between two constant configurations of different types, the process modulo translations is…
Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed…
We analyze the universality classes of phase transitions in a variety of nonlinear voter models. By mapping several models with symmetric absorbing states onto a canonical model introduced in previous studies, we confirm that they exhibit a…
The symmetric exclusion process and the voter model are two interacting particle systems for which a dual finite particle system allows one to characterize its invariant measures. Adding spontaneous births and deaths to the two processes…
This paper is concerned with the following Lotka-Volterra competition system with advection in a periodic habitat \begin{equation*} \begin{cases} \frac{\partial u_1}{\partial t} =d_1(x)\frac{\partial^2 u_1}{\partial…
In this work we investigate the critical behavior of the three dimensional simple-cubic Majority voter model. Using numerical simulations and a combination of two different cumulants we evaluated the critical point with a higher accuracy…
The effect of temporal disorder on systems with up-down Z2 symmetry is studied. In particular, we analyze two well-known families of phase transitions: the Ising and the generalized voter universality classes, and scrutinize the…
Distributed voting is a fundamental topic in distributed computing. In pull voting, in each step every vertex chooses a neighbour uniformly at random, and adopts its opinion. The voting is completed when all vertices hold the same opinion.…
We study the dynamics of an infinite system of point particles of two types. They perform random jumps in $\mathbf{R}^d$ in the course of which particles of different types repel each other whereas those of the same type do not interact.…
The Ising model is well-known for illustrating the fundamental characteristics of phase transitions in closed systems. In this article, we propose a generalization of the two-dimensional Ising model to open systems, considering the…
We study the critical behavior and the out-of-equilibrium dynamics of a two-dimensional Ising model with non-static interactions. In our model, bonds are dynamically changing according to a majority rule depending on the set of closest…
We introduce and analyze a voter-type model on a two-layer multiplex network, where the presence of a state on one layer acts as a catalyst or inhibitor to the propagation of that state on the other layer. Despite the model's simplicity,…
We study the Fleming--Viot particle system in a discrete state space, in the regime of a fast selection mechanism, namely with killing rates which grow to infinity. This asymptotics creates a time scale separation which results in the…
The influence of contrarians on the noisy voter model is studied at the mean-field level. The noisy voter model is a variant of the voter model where agents can adopt two opinions, optimistic or pessimistic, and can change them by means of…
Recently it has been aroused a great interest about explosive (i.e., discontinuous) transitions. They manifest in distinct systems, such as synchronization in coupled oscillators, percolation regime, absorbing phase transitions and more…