Properties of branching exponential flights in bounded domains

Branching random flights are key to describing the evolution of many physical and biological systems, ranging from neutron multiplication to gene mutations. When their paths evolve in bounded regions, we establish a relation between the properties of trajectories starting on the boundary and those starting inside the domain. Within this context, we show that the total length travelled by the walker and the number of performed collisions in bounded volumes can be assessed by resorting to the Feynman-Kac formalism. Other physical observables related to the branching trajectories, such as the survival and escape probability, are derived as well.