  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.
