What is the minimum distance to your doppelganger in an infinite universe

You are a unique combination of atoms arranged in some way In a truly infinite universe, there is a non zero probability that there exists the exact combination more than once (ideally infinite times) This means that any point in time, there exists a minimum distance between you and your 100% clone (atom by atom in every way) in some direction along x,y and z axes in this Universe What is this minimum distance called?