Reversing the drift of the Ehrenfest urn model and three conditionings

We consider a drift-reversed version of the celebrated Ehrenfest urn process with N balls. For this 'dual' process, the boundaries are assumed to be absorbing and so the killing times at the boundaries play a central role. Three natural conditionings on the fixation/extinction events pertaining to this model are investigated. Some spectral information on the conditioned Markoff chains is obtained, allowing us to draw precise new conclusions on their limiting behaviors.