4 diffusion process in the bulk, there is aging behavior at the transition. In addition, we have seen that the expo- nents are in fact not universal, varying with N or the scaled lifetime of the particles on the active site. This is of course very different from the situation that obtains in the superficially similar contact process, which exhibits universal Directed Percolation scaling. increase Δ beyond one, and make the interference ef- fect stronger, thereby reducing the exponent below the original BH value. Actually the precise dimensionless pa- rameter which controls the exponent δ is Δ /ψ 2 ∞ ∝ D Δ, which presents a surprising dependence of the critical ex- ponent δ on the diffusion coefficient ( D ) in the bulk. This is demonstrated in Fig. , where the survival exponent is plotted as a function of Δ. We see that as opposed to the discrete parameter N , now the exponent varies con- tinuously, decreasing with D Δ. Finally we note that the relevance of the limit for which we managed to solve the model analytically is much broader when one considers higher dimension sys- tems. We have studied herein a one dimensional system where the boundary is zero dimensional, while if one con- siders a d dimensional system where the boundary is of dimension d − 1, a line or a membrane, in such a case even if D Δ does not approach zero, the probability that two particles would try to occupy the same site (since there an infinite number of sites on boundary) during the time D Δ is small and this would lead to a larger applicability of our analytical solution. Another type of system where our results could be applied is systems with anomalous diffusion behavior described by the Continu- ous Time Random-Walk model [13], for such systems the results stays valid even if the size of the system is finite as for a finite system with regular diffusion our results are modified for times long enough [11]. In summary, we have extended to finite active site oc- cupancy N and solved analytically the N → ∞ limit of the Barato-Hinrichsen model, yielding the scaling expo- nents of the extinction transition in this limit. We have also show that below a critical fractal dimension for the [2] A. C. Barato, Juan A. Bonachela, C. E. Fiore, H. Hin- richsen and Miguel A. Mu˜ noz, Phys. Rev. E 79 , 041130 (2009). [1] A. C. Barato and H. Hinrichsen, Phys. Rev. Lett. 100 , 165701 (2008). [3] O. Deloubri` ere and F. van Wijland, Phys. Rev. E 65 , 046104 (2002). [4] J. P. Bouchaud, L. F. Cugliandolo, J. Kurchan, and M. M´ ezard, in: A.P. Yound(Ed.), Spin-Glasses and Random Fields p. 161-224 (World Scientific, Singapore, 1997); [5] Henkel M., Pleimling M. and Sanctuary R. (Editors), Ageing and the Glass Transition (Springer, Heidelberg) 2006. [6] L. Cipelletti, S. Manley, R. C. Ball, and D. A. Weitz, Phys. Rev. Lett. 84 , 2275 (2000) [7] L. Silvestri, L. Fronzoni, P. Grigolini, and P. Allegrini Phys. Rev. Lett. 102 , 014502 (2009). [8] D. G. Levitt, Phys. Rev. A 8 , 3050 (1973). [9] S. Redner and K. Kang, Phys. Rev. A 30 , 3362 (1984). [10] G. R. Grimmet and D. R. Stirzaker, Probability and Random Processes (Oxford University Press, New York, 1997). [11] S. Burov and D. A. Kessler (in preparation). [12] R. Metzler and J. Klafter, Phys. Rep. 339 , 1 (2000). FIG. 3: The measured survival exponent δ as a function of Δ, the lifetime of the particle on the active site after it gives birth. The simulations were performed for measurement time t ∼ 10 $^{16}$. FIG. 2: The survival probability, P N S , multiplied by e δ$_{N}$t as a function of time for N = 1, 2 and 3. The values of δ$_{N}$ are as noted in the text. 10 -8 10 -6 10 -4 10 -2 10 0 10 2 10 4 10 6 D  0.1 0.15 0.2 0.25 0.3 10000 1e+08 1e+12 1e+16 t 0 0.2 0.4 0.6 0.8 t P$^{S}$ N N N