Related papers: One-dimensional Voter Model Interface Revisited

The rebellious voter model, introduced by Sturm and Swart (2008), is a variation of the standard, one-dimensional voter model, in which types that are locally in the minority have an advantage. It is related, both through duality and…

Repeated sampling is a standard way to spend test-time compute, but its benefit is controlled by the latent distribution of correctness across examples, not by one-call accuracy alone. We study the binary correctness layer of repeated LLM…

We consider random walks on $\Z^d$ among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of…

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…

We present a modified Brownian motion model for random matrices where the eigenvalues (or levels) of a random matrix evolve in "time" in such a way that they never cross each other's path. Also, owing to the exact integrability of the level…

We study the non-equilibrium dynamics of a one-dimensional interacting particle system that is a mixture of the voter model and the exclusion process. With the process started from a finite perturbation of the ground state Heaviside…

We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…

In this paper we examine a variant of the voter model on a dynamically changing network where agents have the option of changing their friends rather than changing their opinions. We analyse, in the context of dense random graphs, two…

We investigate a variation of the classical voter model in which the set of influencing agents depends on an individual's current opinion. The initial population consists of a random sample of equally sized sub-populations for each state,…

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 consider a simple random walk of length $N$, denoted by $(S_{i})_{i\in \{1,...,N\}}$, and we define $(w_i)_{i\geq 1}$ a sequence of centered i.i.d. random variables. For $K\in\N$ we define $((\gamma_i^{-K},...,\gamma_i^K))_{i\geq 1}$ an…

We address the issue of the reducibility of the dynamics on a multilayer network to an equivalent process on an aggregated single-layer network. As a typical example of models for opinion formation in social networks, we implement the voter…

We consider the two-opinion voter model on a regular random graph with n vertices and degree $d \geq 3$. It is known that consensus is reached on time scale n and that on this time scale the volume of the set of vertices with one opinion…

In this paper we study intermittency for the parabolic Anderson equation $\partial u/\partial t=\kappa\Delta u+\gamma\xi u$ with $u:\mathbb{Z}^d\times[0,\infty)\to\mathbb{R}$, where $\kappa\in[0,\infty)$ is the diffusion constant, $\Delta$…

We study variants of one-dimensional q-color voter models in discrete time. In addition to the usual voter model transitions in which a color is chosen from the left or right neighbor of a site there are two types of noisy transitions. One…

In this paper we present a new and flexible method to show that, in one dimension, various self-repellent random walks converge to self-repellent Brownian motion in the limit of weak interaction after appropriate space-time scaling. Our…

We analyse the effect of agent-dependent heavy-tailed waiting times in the voter model on the complete graph with $N$ vertices. We derive a novel scaling limit and show the existence of a limiting infinite voter model on the slowest…

Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…

We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch\"{u}tz-type formula is derived for the transition probability. We investigate an…

We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and…