In this case the correlation is which is scale invariant for both { α$_{c}$, z$_{c}$ } and { ˜ α$_{r}$ = 1 / (2 γ ) − d/ 2 , z$_{r}$ } . The first invariance can be used to argue that this correlation is a direct consequence of scaling (2), but the scaling form (10) is definitely ambiguous in view of the second invariance. Both sort of dynamics, with and without dilution, are physically realizable; while dilution dynamics is apparently better suited to describe some natural processes, no-dilution dynamics seems to agree better with the numerical simulation of some discrete models as discussed in [16]. Together with the difference in the roughness exponent, very pronounced differences in the auto-correlation and persistence exponents separate the interface behavior in presence and absence of dilution [20]. This reveals that the non-uniqueness of the extension of a Langevin equation to a growing domain implies in turn a universality class bifurcation. One can apply what has been learned in the previous section about growing domains to the radial situation. Including dilution in the radial equation for interface motion yields a different dynamics from the one established by reparametrization invariance. The correlation in this case becomes [16] which is scale invariant for the exponents { ˜ α$_{r}$, z$_{r}$ } but not for { α$_{c}$, z$_{c}$ } . The difference among α$_{r}$ and ˜ α$_{r}$ originates in the memory effects that affect the surface described by reparametrization invariance and disappear by virtue of dilution [16, 20, 22]. The difference between the sets { α$_{r}$, z$_{r}$ } and { ˜ α$_{r}$, z$_{r}$ } , and the classical set { α$_{c}$, z$_{c}$ } is of a different nature. Note that the Langevin dynamics on a growing domain and influenced by dilution gave rise to the random deposition correlation (10): This correlation is invariant to the transformation y → by, t → b $^{z}$t, and h → b $^{α}$h, (13) 〈 h ( y, t ) h ( y $^{′}$, t ) 〉 ∼ tδ ( y − y $^{′}$) . (12) C ( ℓ, ℓ $^{′}$, t ) ∼ t δ ( ℓ − ℓ $^{′}$) J ( t − $^{γ}$ℓ ) , (11) IV. GEOMETRIC CONSTRAINTS 8 C ( y, y $^{′}$, t ) ∼ tδ ( y − y $^{′}$) , (10)