Complexity via replica trick

We consider the complexity of a single-sided AdS black hole as modelled by an end-of-the-world brane. In addition, we present multi-boundary partition functions and matter correlation for such setting. compute using modified replica trick corresponding to "quenched geodesic length" in JT gravity. The late-time behaviour shows saturation constant value order $e^{S_0}$ following period linear growth. Furthermore, show that our approach leads improved result variance complexity, namely it being time-independent at late times. conclude commenting on introduction dynamical branes.