Air carrier pilot reported a luggage cart failed to yield to the airplane during taxi into the MIA gate area. Crew stopped the airplane and then continued to the gate.

Narrative

We entered the ramp area via Spot 6 and stopped perpendicular to the gate (XX) while ground personnel moved to remove a piece of luggage from the safety area. Once the safety area was cleared; we cleared right and left and started our turn into the gate area. After about 40 degrees of turn; a driver towing several luggage carts failed to stop and just blasted his way through our safety area entrance. We were able to stop the aircraft while the driver transited. We continued to the gate once the driver was clear.Cause: The only things that I can think of which would lead to this situation are either 1) the driver was not properly trained on who has the right-of-way in the ramp area (in which case the training program needs to be reevaulated); 2) the driver was property trained but didn't remember/care (in which case the driver needs to be retrained or better supervised); or 3) the driver did not have the situational awareness to know that an aircraft was inbound (in which case the driver needs to be reassigned to a job away from the tarmac as he poses a danger to himself and those around him). Having wing walkers in position to stop ground traffic would have helped prevent this situation from occurring.