弹道湮灭阈值为正
The ballistic annihilation threshold is positive
摘要：
在弹道湮灭过程中，实直线上的粒子具有在$\{-1,0,+1\}$中对称分布的独立速度，并通过碰撞而湮灭。人们普遍认为，在$p=p_{\mathrm c}=0.25$处，在每个粒子最终湮灭和一些粒子永远存活的区域之间存在相变，其中$p$是静止粒子的比例。很容易看出，如果$p>0.5$，一些粒子会存活下来，最近出现了对$p_{\mathrm c}$给出更好上界的严格证明。然而，没有非平凡的下界$p_{\mathrm c}$是以前已知的。我们证明了$p_{\mathrm c}\geq 0.21699$，并给出了一个可比的离散版本的限制。
英文摘要：
In the ballistic annihilation process, particles on the real line have independent speeds symmetrically distributed in $\{-1,0,+1\}$ and are annihilated by collisions. It is widely believed that there is a phase transition at $p=p_{\mathrm c}=0.25$ between regimes where every particle is eventually annihilated and where some particles survive forever, where $p$ is the proportion of stationary particles. It is easy to see that some particles survive if $p>0.5$, and rigorous proofs giving better upper bounds on $p_{\mathrm c}$ have recently appeared. However, no nontrivial lower bound on $p_{\mathrm c}$ was previously known. We prove that $p_{\mathrm c}\geq 0.21699$, and give a comparable bound for a discretised version.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
