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Probabilistic models with nonlocal correlations: Numerical evidence of q-Large Deviation Theory

The correlated probabilistic model introduced and analytically discussed in Hanel et al. (2009) is based on a self-dual transformation of the index q which characterizes a current generalization of Boltzmann–Gibbs statistical mechanics, namely nonextensive statistical mechanics, and yields, in the N→∞ limit, a Q-Gaussian distribution for any chosen value of Q∈[1,3)._x000D_

We show here that, by properly generalizing that self-dual transformation, it is possible to obtain an entire family of such probabilistic models, all of them yielding Qc-Gaussians (Qc≥1) in the N→∞ limit. This family turns out to be isomorphic to the Hanel et al model through a specific monotonic transformation Qc(Q)._x000D_

Then, by following along the lines of Tirnakli et al (2022), we numerically show that this family of correlated probabilistic models provides further evidence towards a q-generalized Large Deviation Theory (LDT), consistently with the Legendre structure of thermodynamics._x000D_

The present analysis deepens our understanding of complex systems (with global correlations among their elements), supporting the conjecture that generic models whose attractors under summation of N strongly-correlated random variables are Q-Gaussians, might always be concomitantly associated with q-exponentials in the LDT sense._x000D_

D.J. Zamora, C. Tsallis, Probabilistic models with nonlocal correlations: Numerical evidence of q-Large Deviation Theory, Physica A: Statistical Mechanics and its Applications 608(1) (2022) 128275

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