  We investigate the long-time behavior of the survival probability of a tagged
particle in a single-file diffusion in a finite interval. The boundary
conditions are of two types: 1) one boundary is absorbing the second is
reflecting, 2) both boundaries are absorbing. For each type of the boundary
conditions we consider two types of initial conditions: a) initial number of
particles N is given, b) initial concentration of particles is given (N is
random). In all four cases the tagged-particle survival probability exhibits
different asymptotic behavior. When the both boundaries are absorbing we also
consider a case of a random interval length (single-file diffusion on a line
with randomly distributed traps). In the latter setting, the initial
concentration of particles has the same effect on the asymptotic decay of the
survival probability as the concentration of traps.
