Tozzi, Arturo (2020) RANDOM WALKS ARE NOT SO RANDOM, AFTER ALL. [Preprint]

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Abstract

Physical and biological phenomena are often portrayed in terms of random walks, white noise, Markov paths, stochastic trajectories with subsequent symmetry breaks. Here we show that this approach from dynamical systems theory is not profitable when random walks occur in phase spaces of dimensions higher than two. The more the dimensions, the more the (seemingly) stochastic paths are constrained, because their trajectories cannot resume to the starting point. This means that high-dimensional tracks, ubiquitous in real world physical/biological phenomena, cannot be operationally treated in terms of closed paths, symplectic manifolds, Betti numbers, Jordan theorem, topological vortexes. This also means that memoryless events disconnected from the past such as Markov chains cannot exist in high dimensions. Once expunged the operational role of random walks in the assessment of experimental phenomena, we take aim to somewhat “redeem” stochasticity. We suggest two methodological accounts alternative to random walks that partially rescue the operational role of white noise and Markov chains. The first option is to assess multidimensional systems in lower dimensions, the second option is to establish a different role for random walks. We diffusely describe the two alternatives and provide heterogeneous examples from boosting chemistry, tunneling nanotubes, backward entropy, chaotic attractors.

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Item Type:	Preprint
Creators:	Creators Email ORCID Tozzi, Arturo tozziarturo@libero.it 0000-0001-8426-4860
Keywords:	noise; topology; time reversed entropy; nonlinear dynamics; memory; brain
Subjects:	Specific Sciences > Complex Systems Specific Sciences > Probability/Statistics General Issues > Theory/Observation
Depositing User:	Dr. Arturo Tozzi
Date Deposited:	10 Oct 2020 17:33
Last Modified:	10 Oct 2020 17:33
Item ID:	18191
Subjects:	Specific Sciences > Complex Systems Specific Sciences > Probability/Statistics General Issues > Theory/Observation
Date:	1 October 2020
URI:	https://philsci-archive.pitt.edu/id/eprint/18191

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