We investigate several
phenomena connected with the movement of particles through a compact
subset B of d-dimensional Eucledian space in a system of infinitely many
particles in statistical equilibrium, where each particle moves independenlly
of the other particles according to the laws of the same symmetric stable
process. In particular, we show that the volume of B governs the rate of flow of
particles through B, and that on the one hand, for transient processes, the
Riesz capacity of B governs the rate at which new particles hit B and at
which particles permanently depart from B, while on the other hand, for
recurrent processes, the rate at which new particles hit B is independent of
B.
