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Distribuciones de probabilidad en las ciencias de la complejidad: una perspectiva contemporánea

Science in the 21st century seems to be governed by novel approaches involving interdisciplinary work, systemic perspectives and complexity theory concepts. These new paradigms force us to leave aside our elder mechanistic approaches and embrace new starting points based on stochasticity, chaoticity, statistics and probability. In this work we review the fundamental ideas of complexity theory and the classic probabilistic models to study complex systems, based on the law of large numbers, central limit theorems and stable distributions. We also talk about power laws as the most common model for phenomena showing long tail distributions and we explore the principal difficulties that arise in practice with this kind of models. We show a novel alternative for the descripition of this type of phenomena and lastly we show two examples that illustrate the applications of this new model.