Peter Mullen, 30, died following an incident on Friday evening involving a number of people.
A large police presence was visible and a cordon was set up outside Edinburgh's Omni Centre following the incidentPolice were called to the incident on Leith Street near the junction with Greenside Row at about 19:45 on Friday.
Det Ch Insp John Morrison said: "Our thoughts are very much with Peter's family and friends at this very difficult time. "We are aware that the area was busy at the time of the incident and we are again encouraging anyone who may have seen or heard a disturbance, to please get in touch," he said.
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