论文标题
多余的副本应该有多大，以使罕见事件可能
How large should be the redundant numbers of copy to make a rare event probable
论文作者
论文摘要
冗余原理通过制作许多类似的随机搜索者的副本，在加速时间中使用概率1来研究罕见事件的框架。但是什么是$ n $大？为了估计域和动力学的几何特性，我们在这里提出了一个标准，基于与激活过程相关的一小部分勘探空间与其他可以终止轨迹的吸收区域相关的探索空间之间的分裂概率。我们获得明确的计算，尤其是当我们与随机模拟比较的域内有一个杀戮区域时。我们还介绍了极端轨迹的例子，并在维度2中杀死。对于大$ n $，最佳轨迹避免在杀戮区域内穿透。最后，我们讨论了细胞生物学的一些应用。
The redundancy principle provides the framework to study how rare events are made possible with probability 1 in accelerated time, by making many copies of similar random searchers. But what is $n$ large? To estimate large $n$ with respect to the geometrical properties of a domain and the dynamics, we present here a criteria based on splitting probabilities between a small fraction of the exploration space associated to an activation process and other absorbing regions where trajectories can be terminated. We obtain explicit computations especially when there is a killing region located inside the domain that we compare with stochastic simulations. We present also examples of extreme trajectories with killing in dimension 2. For a large $n$, the optimal trajectories avoid penetrating inside the killing region. Finally we discuss some applications to cell biology.
