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Characterization and memory effects in stochastic processes

Grant number: 16/03918-7
Support type:Regular Research Grants
Duration: November 01, 2016 - April 30, 2019
Field of knowledge:Physical Sciences and Mathematics - Physics
Principal Investigator:Marco Antonio Alves da Silva
Grantee:Marco Antonio Alves da Silva
Home Institution: Faculdade de Ciências Farmacêuticas de Ribeirão Preto (FCFRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
Assoc. researchers:Alexandre Souto Martinez
Associated grant(s):18/15308-4 - Random walks with strongly correlated memory and applications to biology, AP.R SPRINT


The main purpose of this project is the study of anomalous diffusion in complex non Markovian discrete-time Random Walk systems with strong long range time-memory correlations. Specifically, we focus on systems with full memory and systems with memory damage, the latter being those in which the recent memory has been erased. The question of mapping non-Markovian processes in Markovian processes is discussed. A relation between log-periodic corrections to scaling and anomalous diffusion is analysed through the introduction of pauses in the RW, both in 1D and 2D. Lévy processes are also taken into account by searching for a connection among suitably chosen time-discrete RW memory patterns and Lévy originated processes. The scaling behavior of the Self Avoiding Walk is also addressed using a recently developed method of analysis for studying universality, criticality and conformational properties of systems, with possible applications to polymers, biopolymers and magnetic systems. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
GRANZOTTI, C. R. F.; RIBEIRO, F. L.; MARTINEZ, A. S.; DA SILVA, M. A. A. Persistence length convergence and universality for the self-avoiding random walk. Journal of Physics A-Mathematical and Theoretical, v. 52, n. 7 FEB 15 2019. Web of Science Citations: 0.
CRESSONI, J. C.; VISWANATHAN, G. M.; DA SILVA, M. A. A. Log-periodicity in piecewise ballistic superdiffusion: Exact results. Physical Review E, v. 98, n. 5 NOV 1 2018. Web of Science Citations: 0.

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