论文标题
随机重置下的选民模型
Voter model under stochastic resetting
论文作者
论文摘要
选民模型是基于最近的邻居相互作用的共识形成的玩具模型。一个选民坐在每个顶点的高管晶格（dumension $ d $）中，并且是两个可能的意见州之一。每个选民的意见状态随机翻转，与与选民不同意的最近邻居的比例成正比。如果选民最初是独立的，尚不确定，则知道该模型在且仅当$ d \ leq 2 $时就会达成共识。在本文中，该模型受到随机重置的约束：选民根据固定强度的泊松过程（重置率）独立恢复其初步意见。这种重置处方会导致平均意见状态和模型的两点函数的动力学方程。对于由不确定的选民组成的初始条件，除了一个确定的选民外，单点函数演变为在晶格上存在扩散的随机助行器的概率，该晶格在晶格上的位置随机重置为起源。重置处方会导致非平衡稳态。对于由独立未确定的选民组成的初始状态，稳定状态下的域壁密度以封闭形式表示，这是重置率的函数。当且仅当$ d \ geq 5 $时，此功能在零时可区分。
The voter model is a toy model of consensus formation based on nearest-neighbor interactions. A voter sits at each vertex in a hypercubic lattice (of dimension $d$) and is in one of two possible opinion states. The opinion state of each voter flips randomly, at a rate proportional to the fraction of the nearest neighbors that disagree with the voter. If the voters are initially independent and undecided, the model is known to lead to a consensus if and only if $d\leq 2$. In this paper the model is subjected to stochastic resetting: the voters revert independently to their initial opinion according to a Poisson process of fixed intensity (the resetting rate). This resetting prescription induces kinetic equations for the average opinion state and for the two-point function of the model. For initial conditions consisting of undecided voters except for one decided voter at the origin, the one-point function evolves as the probability of presence of a diffusive random walker on the lattice, whose position is stochastically reset to the origin. The resetting prescription leads to a non-equilibrium steady state. For an initial state consisting of independent undecided voters, the density of domain walls in the steady state is expressed in closed form as a function of the resetting rate. This function is differentiable at zero if and only if $d\geq 5$.
