O paradoxo da superdifusão de uma caminhada aleatória com memória exponencial
The random walk models with temporal correlation (i.e. memory) are of interest in the study of anomalous diffusion phenomena. The random walk and its generalizations are of prominent place in the characterization of various physical, chemical and biological phenomena. The temporal correlation is...
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Formato: | doctoralThesis |
Idioma: | por |
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Universidade Federal do Rio Grande do Norte
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Endereço do item: | https://repositorio.ufrn.br/jspui/handle/123456789/19905 |
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Resumo: | The random walk models with temporal correlation (i.e. memory) are of interest
in the study of anomalous diffusion phenomena. The random walk and its generalizations
are of prominent place in the characterization of various physical, chemical and biological
phenomena. The temporal correlation is an essential feature in anomalous diffusion models.
These temporal long-range correlation models can be called non-Markovian models,
otherwise, the short-range time correlation counterparts are Markovian ones. Within this
context, we reviewed the existing models with temporal correlation, i.e. entire memory,
the elephant walk model, or partial memory, alzheimer walk model and walk model with
a gaussian memory with profile. It is noticed that these models shows superdiffusion with
a Hurst exponent H > 1/2. We study in this work a superdiffusive random walk model
with exponentially decaying memory. This seems to be a self-contradictory statement,
since it is well known that random walks with exponentially decaying temporal correlations
can be approximated arbitrarily well by Markov processes and that central limit
theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes.
The solution to the apparent paradox is that the model is genuinely non-Markovian, due
to a time-dependent decay constant associated with the exponential behavior. In the end,
we discuss ideas for future investigations. |
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