排他过程截断现象的普适性
Universality of cutoff for the Exclusion Process
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中文总结 AI 辅助
本文证明在一般跳跃率条件下，排他过程在固定粒子密度下于时间 $t_{mix}\sim \frac{1}{2}{t}_{rel} \log N$ 出现截断现象，覆盖大环面及顶点传递图，结合多种方法给出普适性证明。
中文摘要 AI 辅助
在关于底层跳跃率的相当一般的条件下，我们证明了具有固定粒子密度的排他过程在时间 $t_{mix}\sim \frac{1}{2}{t}_{rel} \log N$ 处表现出截断现象，其中 $N$ 是体积，${t}_{rel}$ 是单粒子动力学的弛豫时间。我们的结果特别涵盖了在任意固定维度的大离散环面上均匀最近邻跳跃的标准设置，并且更一般地，涵盖了任何具有有界度和多项式发散直径的顶点传递图序列。我们的（简短且完全由人类完成的）证明结合了Wilson方法、八爪鱼不等式、Hamming切片上的傅里叶分析，以及与动力学自然加速变体的Dirichlet形式的尖锐比较。
英文摘要
Under a fairly general condition on the underlying jump rates, we prove that the Exclusion Process with fixed particle density exhibits cutoff at time $t_{mix}\sim \frac{1}{2}{t}_{rel} \log N$, where $N$ is the volume and ${t}_{rel}$ the relaxation time of the single-particle dynamics. Our result covers, in particular, the standard setting of uniform nearest-neighbor jumps on large discrete tori in any fixed dimension and, more generally, on any sequence of vertex-transitive graphs with bounded degree and polynomially diverging diameter. Our (short and entirely human) proof combines Wilson's method, the Octopus Inequality, Fourier analysis on Hamming slices, and a sharp comparison with the Dirichlet form of a natural accelerated variant of the dynamics.
