我们考虑整数段中的简单排除过程$<trans\; data-src="⟦">⟦</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">，</trans>\mathit{<trans\; data-src="N">N个</trans>}<trans\; data-src="⟧">⟧</trans>$具有$\mathit{<trans\; data-src="k">k个</trans>}<trans\; data-src="\le ">\le </trans>\mathit{<trans\; data-src="N">N个</trans>}<trans\; data-src="/">/</trans>\mathrm{<trans\; data-src="2">2</trans>}$粒子和空间不均匀跳跃率。现场有一个微粒$\mathit{<trans\; data-src="x">x个</trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="⟦">⟦</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">，</trans>\mathit{<trans\; data-src="N">N个</trans>}<trans\; data-src="⟧">⟧</trans>$跳转到站点$\mathit{<trans\; data-src="x">x个</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="1">1</trans>}$（如果$\mathit{<trans\; data-src="x">x个</trans>}<trans\; data-src="\ge ">\ge </trans>\mathrm{<trans\; data-src="2">2</trans>}$)按速率$\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="-">-</trans>{\mathit{<trans\; data-src="\omega ">\omega </trans>}}_{\mathit{<trans\; data-src="x">x个</trans>}}$和现场$\mathit{<trans\; data-src="x">x个</trans>}\mathbf{<trans\; data-src="+">+</trans>}\mathrm{<trans\; data-src="1">1</trans>}$（如果$\mathit{<trans\; data-src="x">x个</trans>}<trans\; data-src="\le ">\le </trans>\mathit{<trans\; data-src="N">N个</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="1">1</trans>}$)按速率${\mathit{<trans\; data-src="\omega ">\omega </trans>}}_{\mathit{<trans\; data-src="x">x个</trans>}}$如果目标站点未被占用。序列$\mathit{<trans\; data-src="\omega ">\omega </trans>}<trans\; data-src="=">=</trans>{<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="\omega ">\omega </trans>}}_{\mathit{<trans\; data-src="x">x个</trans>}}<trans\; data-src=")">)</trans>}_{\mathit{<trans\; data-src="x">x个</trans>}<trans\; data-src="\in ">\in </trans>\mathbb{<trans\; data-src="Z">Z轴</trans>}}$由IID抽样从支持度远离零和一的概率定律中选择（换句话说，随机环境满足一致椭圆条件）。我们进一步假设$\mathbb{<trans\; data-src="E">E类</trans>}<trans\; data-src="[">[</trans><trans\; data-src="log">日志</trans>{\mathit{<trans\; data-src="\rho ">\rho </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="]">]</trans><trans\; data-src="<"><</trans>\mathrm{<trans\; data-src="0">0</trans>}$哪里${\mathit{<trans\; data-src="\rho ">\rho </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=":">:</trans><trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="-">-</trans>{\mathit{<trans\; data-src="\omega ">\omega </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="/">/</trans>{\mathit{<trans\; data-src="\omega ">\omega </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}$这意味着我们的粒子有向右移动的趋势。我们证明了在这种情况下，排除过程的混合时间增长为N个。更确切地说，对于具有${\mathit{<trans\; data-src="N">N个</trans>}}^{\mathit{<trans\; data-src="\beta ">\beta </trans>}\mathbf{<trans\; data-src="+">+</trans>}\mathit{<trans\; data-src="o">o个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=")">)</trans>}$粒子，其中$\mathit{<trans\; data-src="\beta ">\beta </trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">，</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="]">]</trans>$，我们有大的N个渐近的

$${\mathit{<trans\; data-src="N">N个</trans>}}^{<trans\; data-src="max">最大值</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">，</trans>\frac{\mathrm{<trans\; data-src="1">1</trans>}}{\mathit{<trans\; data-src="\lambda ">\lambda </trans>}}<trans\; data-src=",">，</trans>\mathit{<trans\; data-src="\beta ">\beta </trans>}\mathbf{<trans\; data-src="+">+</trans>}\frac{\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="2">2</trans>}\mathit{<trans\; data-src="\lambda ">\lambda </trans>}}<trans\; data-src=")">)</trans>\mathbf{<trans\; data-src="+">+</trans>}\mathit{<trans\; data-src="o">o个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=")">)</trans>}<trans\; data-src="\le ">\le </trans>{\mathit{<trans\; data-src="t">吨</trans>}}_{\mathrm{<trans\; data-src="mix">混合</trans>}}^{\mathit{<trans\; data-src="N">N个</trans>}<trans\; data-src=",">，</trans>\mathit{<trans\; data-src="k">k个</trans>}}<trans\; data-src="\le ">\le </trans>{\mathit{<trans\; data-src="N">N个</trans>}}^{\mathit{<trans\; data-src="C">C类</trans>}\mathbf{<trans\; data-src="+">+</trans>}\mathit{<trans\; data-src="o">o个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=")">)</trans>}<trans\; data-src=",">，</trans>$$

哪里$\mathit{<trans\; data-src="\lambda ">\lambda </trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$是这样的$\mathbb{<trans\; data-src="E">E类</trans>}<trans\; data-src="[">[</trans>{\mathit{<trans\; data-src="\rho ">\rho </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathit{<trans\; data-src="\lambda ">\lambda </trans>}}<trans\; data-src="]">]</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}$($\mathit{<trans\; data-src="\lambda ">\lambda </trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="\infty ">\infty </trans>}$如果方程没有正根）和C类是一个常数，取决于ω。我们推测，我们的下限在亚多项式校正之前是很尖锐的。