Related papers: Persistence in the Voter model: continuum reaction…

We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \ge 3$. Combining this result with…

We compute the persistence for the $2d$-diffusion equation with random initial condition, i.e., the probability $p_0(t)$ that the diffusion field, at a given point ${\bf x}$ in the plane, has not changed sign up to time $t$. For large $t$,…

The persistence properties of a set of random walkers obeying the A+B -> 0 reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability, P(t), that an…

The persistence exponent $\theta_o$ for the simple diffusion equation ${\phi}_t({\it x},t) = \triangle \phi (x,t)$ , with random Gaussian initial condition {\color{red},} has been calculated exactly using a method known as selective…

We investigate coarsening and persistence in the voter model by introducing the quantity $P_n(t)$, defined as the fraction of voters who changed their opinion n times up to time t. We show that $P_n(t)$ exhibits scaling behavior that…

In the $q$-voter model, the voter at $x$ changes its opinion at rate $f_x^q$, where $f_x$ is the fraction of neighbors with the opposite opinion. Mean-field calculations suggest that there should be coexistence between opinions if $q<1$ and…

We study the persistence probability for some discrete-time, time-reversible processes. In particular, we deduce the persistence exponent in a number of examples: first, we deal with random walks in random sceneries (RWRS) in any dimension…

We study the dynamics of a class of two dimensional stochastic processes, depending on two parameters, which may be interpreted as two different temperatures, respectively associated to interfacial and to bulk noise. Special lines in the…

We obtain \theta_p(q) = 2\theta_s(q) for one-dimensional q-state ferromagnetic Potts models evolving under parallel dynamics at zero temperature from an initially disordered state, where \theta_p(q) is the persistence exponent for parallel…

We study a d-dimensional system of diffusing particles that on contact either annihilate with probability 1/(q-1) or coagulate with probability (q-2)/(q-1). In 1-dimension, the system models the zero temperature Glauber dynamics of domain…

In systems which exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random walk models. Provided the decay of correlations is fast enough, one can ignore memory…

We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which…

We show that the persistence probability $P(t,L)$, in a coarsening system of linear size $L$ at a time $t$, has the finite size scaling form $P(t,L)\sim L^{-z\theta}f(\frac{t}{L^{z}})$ where $\theta$ is the persistence exponent and $z$ is…

We formulate and investigate the nonlinear $q$-voter model (which as special cases includes the linear voter and the Sznajd model) on a one dimensional lattice. We derive analytical formula for the exit probability and show that it agrees…

In elections, the vote shares or turnout rates show a strong spatial correlation. The logarithmic decay with distance suggests that a 2D noisy diffusive equation describes the system. Based on the study of U.S. presidential elections data,…

We examine a generalized KPP equation with a ``$q$-diffusion", which is a framework that unifies various standard linear diffusion regimes: Fickian diffusion ($q = 0$), Stratonovich diffusion ($q = 1/2$), Fokker-Planck diffusion ($q = 1$),…

The Dantzig selector for a special parametric model of diffusion processes is studied in this paper. In our model, the diffusion coefficient is given as the exponential of the linear combination of other processes which are regarded as…

We consider the d-dimensional diffusion equation for a field phi(x,t) with random initial condition, and observe that, when appropriately scaled, phi(0,t) is Gaussian and Markovian in the limit d->0. This leads via the Majumdar-Sire…

In this paper, we consider the voter model with popularity bias. The influence of each node on its neighbors depends on its degree. We find the consensus probabilities and expected consensus times for each of the states. We also find the…

We discuss the exit probability of the one dimensional $q$-voter model and present tools to obtain estimates about this probability both through simulations in large networks (around $10^7$ sites) and analyticaly in the limit where the…