Related papers: Stretched Exponential Relaxation in the Biased Ran…
In this paper, we extend the central limit theorem of the occupation time of the voter model on the lattice $\mathbb{Z}^d$ given in \cite{Cox1983} to the sample path case for $d\geq 3$. The proof of our main result utilizes the resolvent…
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…
A simple model of an irreversible process is introduced. The equation of iterations in the model includes a noise generation term. We study the properties of the system when the noise generation term is a stochastic process (e.g. a random…
The utilitarian distortion framework evaluates voting rules by their worst-case efficiency loss when voters have cardinal utilities but express only ordinal rankings. Under the classical model, a longstanding tension exists: Plurality,…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
Dynamic relaxation of the XY model and fully frustrated XY model quenched from an initial ordered state to the critical temperature or below is investigated with Monte Carlo methods. Universal power law scaling behaviour is observed. The…
We re-examine the procedure of adiabatic elimination of fast relaxing variables near a bifurcation point when some of the parameters of the system are stochastically modulated. Approximate stationary solutions of the Fokker-Planck equation…
There are many materials whose dielectric properties are described by a stretched exponential, the so-called Kohlrausch-Williams-Watts (KWW) relaxation function. Its physical origin and statistical-mechanical foundation have been a matter…
Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random…
The coarsening exponents describing the growth of long-range order in systems quenched from a disordered to an ordered phase are discussed in terms of the decay rate, omega(k), for the relaxation of a distortion of wavevector k applied to a…
We consider two independent stationary random walks on large random regular graphs of degree $k\geq 3$ with $N$ vertices. On these graphs, the exponential approximations of the meeting times are known to follow from existing methods and…
We propose a modified voter model with locally conserved magnetization and investigate its phase ordering dynamics in two dimensions in numerical simulations. Imposing a local constraint on the dynamics has the surprising effect of speeding…
We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
In this paper we consider the model of phase relaxation introduced in [22], where an asymptotic analysis is performed toward an integral formulation of the Stefan problem when the relaxation parameter approaches zero. Assuming the natural…
Many theoretical studies of the voter model (or variations thereupon) involve order parameters that are population-averaged. While enlightening, such quantities may obscure important statistical features that are only apparent on the level…
The notions of noise sensitivity and stability were recently extended for the voter model. In this model, the vertices of a graph have opinions that are updated by uniformly selecting edges. We further extend stability results to different…
Our recently developed "unbiased" extremum seeking (uES) algorithms ensure perfect convergence to the optimum at a user-assigned exponential rate or, more powerfully, within a user-prescribed time. Unlike classical approach, these…
We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter $k \ge 0$, in addition to its $+$ or $-$ opinion state. The evolution of the…
We study the noisy voter model using a specific non-linear dependence of the rates that takes into account collective interaction between individuals. The resulting model is solved exactly under the all-to-all coupling configuration and…