论文标题
一维离散时间促进对称排除过程的静止状态
Stationary States of the One-Dimensional Discrete-Time Facilitated Symmetric Exclusion Process
论文作者
论文摘要
我们描述了$ \ mathbb {z} $的促进排除过程的极端翻译不变的固定态（ETIS）状态。在此模型中，每个整数时间都有一个占用的站点上的所有粒子跳到空邻居站点，如果两个粒子试图跳入同一空站点，我们会选择一个随机成功。 ETIS状态在密度上是质量不同的$ρ<1/2 $，$ρ= 1/2 $和$ 1/2 <ρ<1 $，但是在每个密度区域中，我们发现可能将其分组为家庭，每个状态都与$ \ \ \ \ \ \ \ \ \ \ \ \ \}^Z $ \ \ {0,1^{Z $} $ \ \ \ \ \ {0,1^{Z {Z {对于$ρ<1/2 $，有一个这样的家庭，其中包含所有厄基德州，其中两个相邻占领地点的概率为零。对于$ρ= 1/2 $，有两个家庭，其中配置分别向左和右转换为持续的速度2。对于高密度的情况，有一个连续的家庭。我们表明，所有Etis状态都处于密度$ρ\ le1/2 $属于这些家族，并且在高密度下也没有其他ETIS状态的猜想。我们还研究了如果猜想失败，可能发生的ETIS状态。
We describe the extremal translation invariant stationary (ETIS) states of the facilitated exclusion process on $\mathbb{Z}$. In this model all particles on sites with one occupied and one empty neighbor jump at each integer time to the empty neighbor site, and if two particles attempt to jump into the same empty site we choose one randomly to succeed. The ETIS states are qualitatively different for densities $ρ<1/2$, $ρ=1/2$, and $1/2<ρ<1$, but in each density region we find states which may be grouped into families, each of which is in natural correspondence with the set of all ergodic measures on $\{0,1\}^{\mathbb{Z}}$. For $ρ<1/2$ there is one such family, containing all the ergodic states in which the probability of two adjacent occupied sites is zero. For $ρ=1/2$ there are two families, in which configurations translate to the left and right, respectively, with constant speed 2. For the high density case there is a continuum of families. We show that all ETIS states at densities $ρ\le1/2$ belong to these families, and conjecture that also at high density there are no other ETIS states. We also study the possible ETIS states which might occur if the conjecture fails.
