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- W4323922846 abstract "The late time behavior of random walk models (binary chains) with non-linear long-range correlations is determined analytically. It is well established in the physics literature that if the jumping probability of a walker towards a particular direction (say, to the right) decreases linearly with the fraction of steps taken in this direction in the past, p(x,t)−1/2∝−x/t, then the asymptotic late-time variance of the system grows linearly with time as in normal (non-correlated) diffusion processes: σ2(t→∞)∝t1 [here {x,t} are respectively the location of the walker and the evolution time]. In the present paper we prove, using analytical techniques, that if the jumping probability of a walker towards a particular direction decreases non-linearly with the fraction of steps taken in this direction in the past, p(x,t)−1/2∝−sgn(x)(|x|/t)β with β<1, then the behavior of the system undergoes a dynamical phase-transition into a sub-diffusive state in which the asymptotic variance grows slower in time: σ2(t→∞)∝tδ(β) with δ(β)≡2β/(1+β)<1. In particular, it is proved that the power-law index δ(β) vanishes in the highly non-linear β≪1 regime." @default.
- W4323922846 created "2023-03-12" @default.
- W4323922846 creator A5046640072 @default.
- W4323922846 date "2023-05-01" @default.
- W4323922846 modified "2023-09-25" @default.
- W4323922846 title "Analytic treatment of random walk models with non-linear history-dependent correlations" @default.
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- W4323922846 doi "https://doi.org/10.1016/j.aop.2023.169271" @default.
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