Air carrier Captain reported during taxi to the gate another air carrier taxied in front of them at a high rate of speed and nearly missed impacting the reporter's aircraft.

Narrative

We were on an inbound taxi to our gate. We were instructed take Taxiway LL and then turn west onto Taxiway A behind an Aircraft westbound on A. That aircraft now in front of us halted momentarily on A as it was going into the gate. We subsequently halted as well with our nose well into Taxi A. Just as that Aircraft cleared off A to park and I was attempting to throttle forward; an Aircraft came westbound on Taxiway A at high speed and crossed right in front with his left wing just missing our radome by several feet. It did not appear the Captain of the Aircraft was looking in our direction at any time. My First officer was yelling at the Aircraft and alerting the Ground Controller throughout the whole incident. The Controller stated he would talk to the pilot of the Aircraft. My alert First Officer was able to see this unfolding in advance and did everything he could to prevent the mishap. It did not appear that the Aircraft (flight # unknown) was aware of anything; before or after the incident.Cause: I don't know; because I don't fully know what that other planes clearance was.Suggestions: Slower taxi speed. Monitor ATC always when on a taxiway.