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We investigate quantum persistence by analyzing amplitude and phase fluctuations of the wave function governed by the time-dependent free-particle Schr\"odinger equation. The quantum system is initialized with local random uncorrelated…

Statistical Mechanics · Physics 2025-05-09 Cheng Ma , Omar Malik , G. Korniss

We address the persistence under a perturbation of stationary pulse solutions of some reaction-diffusion type equations in dimensions d=2,3 and evaluate the asymptotic approximations of such pulses to the leading order in the parameter of…

Analysis of PDEs · Mathematics 2024-12-24 Vitali Vougalter

We calculate the diffusion coefficients of persistent random walks on cubic and hypercubic lattices, where the direction of a walker at a given step depends on the memory of one or two previous steps. These results are then applied to study…

Statistical Mechanics · Physics 2013-02-07 Thomas Gilbert , Huu Chuong Nguyen , David P Sanders

We investigate the coarsening kinetics in a long-range variant of the Persistent Voter Model in space dimension $d=1$ and 2. In this model agents can hold two confidence levels, normal and zealot. If normal, agents take the opinion of…

Statistical Mechanics · Physics 2026-03-17 Jeferson J. Arenzon , F. Corberi , W. G. Dantas , L. Smaldone

We consider an arbitrary Gaussian Stationary Process X(T) with known correlator C(T), sampled at discrete times T_n = n \Delta T. The probability that (n+1) consecutive values of X have the same sign decays as P_n \sim \exp(-\theta_D T_n).…

Statistical Mechanics · Physics 2009-11-07 George C. M. A Ehrhardt , Alan J. Bray

Opinion diffusion is a crucial phenomenon in social networks, often underlying the way in which a collective of agents develops a consensus on relevant decisions. The voter model is a well-known theoretical model to study opinion spreading…

Multiagent Systems · Computer Science 2024-03-14 Luca Becchetti , Vincenzo Bonifaci , Emilio Cruciani , Francesco Pasquale

We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions d1 ~ 26 and…

Statistical Mechanics · Physics 2009-01-23 T. J. Newman , Will Loinaz

We introduce a non-linear variant of the voter model, the q-voter model, in which q neighbors (with possible repetition) are consulted for a voter to change opinion. If the q neighbors agree, the voter takes their opinion; if they do not…

Physics and Society · Physics 2009-11-27 C. Castellano , M. A. Munoz , R. Pastor-Satorras

We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at…

Statistical Mechanics · Physics 2014-07-18 P. L. Krapivsky

We study the bidimensional voter model on a square lattice with numerical simulations. We demonstrate that the evolution takes place in two distinct dynamic regimes; a first approach towards critical site percolation and a further approach…

Statistical Mechanics · Physics 2015-10-14 Alessandro Tartaglia , Leticia F. Cugliandolo , Marco Picco

The voter model on $\mathbb{Z}^d$ is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When $d \geq 3$, the set of…

Probability · Mathematics 2016-02-19 Balazs Rath , Daniel Valesin

We present in this paper an approximation that is able to give an analytical expression for the exit probability of the $q$-voter model in one dimension. This expression gives a better fit for the more recent data about simulations in large…

Physics and Society · Physics 2014-08-13 André Martin Timpanaro , Serge Galam

We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…

Analysis of PDEs · Mathematics 2025-03-07 Nathanaël Boutillon , Luca Rossi

It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in…

Probability · Mathematics 2010-02-11 Alain Comtet , Yves Tourigny

The problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d. We consider the case where the traps are initially randomly distributed in space, with uniform density rho, and derive upper and…

Statistical Mechanics · Physics 2009-11-07 R. A. Blythe , A. J. Bray

We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms,…

Probability · Mathematics 2025-06-24 Manuel González-Navarrete

We present a scheme to accurately calculate the persistence probabilities on sequences of $n$ heights above a level $h$ from the measured $n+2$ points of the height-height correlation function of a fluctuating interface. The calculated…

Statistical Mechanics · Physics 2010-03-10 J. M. J. van Leeuwen , V. W. A. de Villeneuve , H. N. W. Lekkerkerker

We analyse conditions for an evolution equation with a drift and fractional diffusion to have a Holder continuous solution. In case the diffusion is of order one or more, we obtain Holder estimates for the solution for any bounded drift. In…

Analysis of PDEs · Mathematics 2011-04-26 Luis Silvestre

We study the following 1D two-species reaction diffusion model : there is a small concentration of B-particles with diffusion constant $D_B$ in an homogenous background of W-particles with diffusion constant $D_W$; two W-particles of the…

Condensed Matter · Physics 2009-10-28 Cécile Monthus

We consider the voter model with binary opinions on a random regular graph with $n$ vertices of degree $d \geq 3$, subject to a rewiring dynamics in which pairs of edges are rewired, i.e., broken into four half-edges and subsequently…