The noisy voter-exclusion process

Cutoff for the noisy voter model

Given a continuous time Markov Chain $\{q(x,y)\}$ on a finite set $S$, the associated noisy voter model is the continuous time Markov chain on $\{0,1\}^S$, which evolves in the following way: (1) for each two sites $x$ and $y$ in $S$, the state at site $x$ changes to the value of the state at site $y$ at rate $q(x,y)$; (2) each site rerandomizes its state at rate 1. We show that if there is a uniform bound on the rates $\{q(x,y)\}$ and the corresponding stationary distributions are almost uniform, then the mixing time has a sharp cutoff at time $\log|S|/2$ with a window of order 1. Lubetzky an…

带噪声选民模型密度过程的渐近行为

Asymptotic behaviour of the noisy voter model density process

本文研究带噪声选民模型密度过程在时间趋于无穷时的渐近行为，证明噪声参数较小时归一化密度收敛于高斯随机变量、较大时收敛于伯努利随机变量，并在完全图、环、环面和超立方体上确定了临界噪声速率。

Ergodicity and Percolation for Variants of One-dimensional Voter Models

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 is bulk nucleation where a new random color is chosen. The other is boundary nucleation where a random color is chosen only if the two neighbors have distinct colors. We prove under a variety of conditions on q and the magnitudes of the two noise parameters that the system is ergodic, i.e., there is convergence to a unique invariant distribution. The methods…

Coalescing and branching simple symmetric exclusion process

Motivated by kinetically constrained interacting particle systems (KCM), we consider a reversible coalescing and branching simple exclusion process on a general finite graph $G=(V,E)$ dual to the biased voter model on $G$. Our main goal are tight bounds on its logarithmic Sobolev constant and relaxation time, with particular focus on the delicate slightly supercritical regime in which the equilibrium density of particles tends to zero as $|V|\rightarrow \infty$. Our results allow us to recover very directly and improve to $\ell^p$-mixing, $p\ge 2$, and to more general graphs, the mixing time r…

具有一般初始条件的噪声选民模型

The noisy voter model with general initial conditions

本文研究一般图上的噪声选民模型，证明其截止时间由初始状态的自相关函数显式决定，并据此证实交替初始条件在1D Ising模型中对所有噪声值渐近最快。

对称噪声投票模型中任意初始和边界条件的平均首次通过时间

Mean First Passage Time of the Symmetric Noisy Voter Model with Arbitrary Initial and Boundary Conditions

本研究探讨了对称噪声投票模型中任意初始和边界条件对平均首次通过时间的影响，推导出精确解析表达式并验证了Kramers定律的适用性。

Particle Systems arising from an anti-ferromagnetic Ising model

We study a low temperature anisotropic anti-ferromagnetic 2D Ising model through the guise of a certain dimer model. This model has a bijection with a one-dimensional particle system equipped with creation and annihilation. In the thermodynamic limit, we determine the explicit phase diagrams as functions of temperature and anisotropy. Two values of the anisotropy are of particular interest - the 'critical' value and the 'independent' value. At independence, the particle system has the same distribution as the two colored noisy voter model. Its limiting measure under a natural scaling window is…

量子对称简单排斥过程在连续域中的表现与自由过程

The Quantum Symmetric Simple Exclusion Process in the Continuum and Free Processes

本文提出量子对称简单排斥过程在连续域中的表述，探讨其作为非交换过程的特性，并为宏观波动理论的量子扩展奠定基础。

Hecke 代数的表示与交互粒子系统的 Markov 对偶性

Representations of Hecke algebras and Markov dualities for interacting particle systems

本文对生成元由双点位等幂算子之和构成的连续时间 Markov 过程进行分类，揭示了其与 Hecke 代数不可约表示的联系，并通过标准的 Baxterisation 过程导出了不守恒粒子数系统的 Young-Baxter 方程新解。

具有噪声交互的非线性意见动力学的相变

Phase Transition of a Non-Linear Opinion Dynamics with Noisy Interactions

本文为二元 undecided dynamics 引入均匀消息噪声，证明亚稳态共识在 p=1/6 处发生相变，并将其等价于含固执智能体的模型。