  The self-repelling Brownian polymer model (SRBP) initiated by Durrett and
Rogers in [Durrett-Rogers (1992)] is the continuous space-time counterpart of
the myopic (or 'true') self-avoiding walk model (MSAW) introduced in the
physics literature by Amit, Parisi and Peliti in [Amit-Parisi-Peliti (1983)].
In both cases, a random motion in space is pushed towards domains less visited
in the past by a kind of negative gradient of the occupation time measure.
  We investigate the asymptotic behaviour of SRBP in the non-recurrent
dimensions. First, extending 1-dimensional results from [Tarres-Toth-Valko
(2009)], we identify a natural stationary (in time) and ergodic distribution of
the environment (essentially, smeared-out occupation time measure of the
process), as seen from the moving particle. As main result we prove that in
three and more dimensions, in this stationary (and ergodic) regime, the
displacement of the moving particle scales diffusively and its finite
dimensional distributions converge to those of a Wiener process. This result
settles part of the conjectures (based on non-rigorous renormalization group
arguments) in [Amit-Parisi-Peliti (1983)].
  The main tool is the non-reversible version of the Kipnis--Varadhan-type CLT
for additive functionals of ergodic Markov processes and the graded sector
condition of [Sethuraman-Varadhan-Yau (2000)].
