Air carrier Captain reported a critical ground conflict while taxiing clear of the runway when an aircraft taxied in front of them at a high rate of speed. The Captain had to apply brakes sharply to avoid the other aircraft and suggested that Ramp Control should have given a traffic advisory before clearing them to taxi.

Narrative

After landing on Runway XXR at ZZZ we had a loss of separation with Aircraft Y while taxiing to the gate. We vacated Runway XXR at Taxiway XX and were instructed to contact Ramp Control. The First Officer was heads down changing frequencies and I was setting the exterior lights for taxi after clearing the active runway. The Ramp Controller instructed us to enter the ramp via Taxiway XY taxi XZ then the outer line to the gate. They then added that we would pass behind Aircraft Y (or go behind Aircraft Y). I was focused on looking at where we were going to be heading and where the other airplane would be on the left; when I caught movement out of my peripheral vision coming from the right and sharply applied the brakes. The First Officer spotted the other aircraft racing toward us at the same time and warned me as well. Aircraft Y passed within 25 ft. of the nose of our aircraft at what we thought was an excessive speed.After arriving at the gate and disembarking the passengers I contacted Operations and asked for a phone number for the Ramp Controller. At first they were confused and then they didn't want to give me the number; so I passed mine along to them and asked Ramp to call me; as I didn't want to 'air dirty laundry in public.' I explained to the Ramp Controller that we had nearly had a collision with Aircraft Y and that it might be more helpful in the future to give the traffic advisory before giving us a taxi clearance. I tried to be as pleasant and non accusatory as possible. The Controller seemed to appreciate the suggestion but said that he'd been doing this job for a while. He also said that Aircraft Y was known to 'speed' while on the ramp.I have no confidence that my suggestion to give the restriction to the taxi clearance or traffic advisory; eg. Give way to Aircraft Y from the right; then taxi.... or instruct inbound aircraft to hold short until traffic has passed will be adopted without elevating this issue to a higher level. The Ramp Controller called me from XXX.XXX.XXXX; but I don't know if that's a personal phone or an office line.I can be more aware of the structural blind spot caused by the First Officer and the size of the window when looking for traffic approaching from the right. ZZZ Ramp Controllers could benefit from refresher training on proper radio phraseology eg. give way to..... vs you'll go behind.... and reiterate the importance of pointing out converging traffic before issuing a clearance to proceed into the path of an oncoming aircraft. Aircraft Y could be reminded to adjust their taxi speeds based on environmental conditions and traffic so as to give everyone operating on the ramp greater time to react to threats.