School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6997801, Israel.
Center for the Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel.
Phys Rev Lett. 2019 Jan 18;122(2):020602. doi: 10.1103/PhysRevLett.122.020602.
First passage under restart with branching is proposed as a generalization of first passage under restart. Strong motivation to study this generalization comes from the observation that restart with branching can expedite the completion of processes that cannot be expedited with simple restart; yet a sharp and quantitative formulation of this statement is still lacking. We develop a comprehensive theory of first passage under restart with branching. This reveals that two widely applied measures of statistical dispersion-the coefficient of variation and the Gini index-come together to determine how restart with branching affects the mean completion time of an arbitrary stochastic process. The universality of this result is demonstrated and its connection to extreme value theory is also pointed out and explored.
提出分支重启下的首次通过作为重启下首次通过的推广。研究这种推广的强烈动机来自于这样一个观察结果：分支重启可以加速那些不能通过简单重启来加速的过程的完成；然而，这个说法的一个尖锐和定量的表述仍然缺乏。我们发展了分支重启下首次通过的综合理论。这表明，两种广泛应用的统计离散度度量——变异系数和基尼指数——共同决定了分支重启如何影响任意随机过程的平均完成时间。该结果的普遍性得到了证明，并指出和探讨了其与极值理论的联系。
