发表机构
Yonsei University; Seoul National University（延世大学; 首尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究高维环面上促进排除过程的循环结构，证明密度阈值导致唯一或多循环类，并给出小密度下多对数吸收时间与中等密度下多项式下界，揭示双重相变。
AI 中文摘要
本文研究了在边长$N$的$d$维离散环面上的促进排除过程（FEP），其中$d\ge2$。对于固定密度$\rho\in(0,1)$的伯努利初始数据，我们首先证明，当$\rho>1-2^{-d}$时，初始构型所选择的粒子数扇区以高概率具有唯一的活跃循环类；当$\rho<1-2^{-d}$时，则存在多个循环类。随后我们证明，对于足够小的$\rho$，该过程以高概率在$N$的多对数时间内达到吸收态（即单例循环类）。相反，对于$\rho\in(1/2,3/4)$且$N$为偶数的情况，我们建立了达到循环集所需时间的多项式下界。这些结果为双重相变提供了有力证据，类似于接触过程、激活随机游走和随机沙堆模型中的吸收态相变。据我们所知，这是对二维及以上维度FEP吸收时间和瞬态时间的首批严格估计。
英文摘要
In this article, we study the facilitated exclusion process (FEP) on the $d$-dimensional discrete torus of side length $N$, with $d\ge2$. For Bernoulli initial data with a fixed density $ρ\in(0,1)$, we first prove that, with high probability, the particle-number sector selected by the initial configuration has a unique active recurrent class if $ρ>1-2^{-d}$ and multiple recurrent classes if $ρ<1-2^{-d}$. We then show that, for sufficiently small $ρ$, the process reaches an absorbing state (a singleton recurrent class) within a poly-logarithmic time in $N$ with high probability. In contrast, for $ρ\in(1/2,3/4)$ and even $N$, we establish a polynomial lower bound on the time required to reach the recurrent set. These results provide strong evidence for a double phase transition, analogous to absorbing-state phase transitions in the contact process, activated random walks, and stochastic sandpiles. To our knowledge, these are the first rigorous estimates for absorption and transient times for the FEP in dimensions two and higher.
Comments26 pages, 3 figures
