Renewal and memory properties in the random growth of surfaces Page: 7
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FIG. 5: Probability distribution of ( >R, for R=0 (square), R=1 (circle) and R=5 (triangle).
5000 10000 15000 20000
25000 30000 35000 40000
FIG. 6: Probability distribution of waiting times of ( >R, for R= 0, R= 1 and R=10.
V. CONCLUDING REMARKS
This paper shows how to reconcile a perspective based on memory with one based on renewal non-Poisson processes.
To a first sight, these two visions can be perceived as being incompatible. For instance, the adoption of the FBM
theory adopted by some authors to account for persistency [37, 38, 39] seems to conflict with the renewal approach.
On the contrary, in accordance with the recent result of Ref.  this paper shows that the cooperative nature of the
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Cakir, Rasit; Grigolini, Paolo & Ignaccolo, Massimiliano. Renewal and memory properties in the random growth of surfaces, article, February 4, 2008; (digital.library.unt.edu/ark:/67531/metadc132977/m1/7/: accessed August 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.