# gst: rich behaviors from stochastic walking with variable long jumps.

AA << propose a generalized model where the random walker takes stochastic jumps of lengths proportional to its present position with certain probability, otherwise it makes forward and backward jumps of fixed (unit) length with given rates. The model exhibits a rich stochastic dynamic behavior.  (AA) obtain exact analytic results for the first two moments of the walker's displacement and show that a phase transition from a diffusive to superdiffusive regime occurs if the stochastic jumps of lengths that are twice (or more) of its present positions are allowed. This phase transition is accompanied by a reentrant diffusive behavior. >> 

Upendra Harbola. Stochastic walker with variable long jumps. Phys. Rev. E 108, 014135. July 28, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.014135 

Also: walk, noise, fluctuations, dance,  in: https://www.inkgmr.net/kwrds.html

Keywords: gst, walks, random walks, noise, fluctuations

# gst: dissolve into randomness, the kinetics

AA << have developed mathematical tools that send that shot across the bow-they determine when randomness emerges in any stochastic (random) system, answering a long-standing question: When does randomness set in during a random walk? >>

<< We are trying to describe an effect as exactly as possible irrespective of the cause. >> Rajan K. Chakrabarty

<< physicists normally solve problems by mathematically describing a cause and effect and marrying the two for a solution. But this new tool cares nothing about the cause, only about mathematically capturing the effect. >>

Tony Fitzpatrick. New tools reveal prelude to chaos. Washington University in St. Louis. Jun 6, 2018

https://m.phys.org/news/2018-06-tools-reveal-prelude-chaos.html  

Pai Liu, William R. Heinson, et al. Establishing the kinetics of ballistic-to-diffusive transition using directional statistics. Phys. Rev. E 97, 042102. Apr 4, 2018.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.042102