Gómez Garay, Ignacio T. (2021) Procesos de reseteo estocástico en modelos de sistemas socioeconómicos / Stochastic reset processes in models of socioeconomic systems. Maestría en Ciencias Físicas, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
Los sistemas de agentes multiplicativos con reseteo estocástico son un modelo basado en agentes (MBA) conocido por generar distribuciones de probabilidad estacionarias de ley de potencia para los recursos individuales. Esta propiedad se considera valiosa en la literatura dada la abundancia de variables que presentan distribución de ley de potencias en diversos campos como la biología, economía, lingüística, entre otros. En esta Tesis de Maestría introducimos distintos esquemas de acoplamiento en el modelo original, tanto cooperativos como competitivos, lineales como no lineales, globales y distribuidos en el espacio, y estudiamos las propiedades estadísticas emergentes de cada caso. En particular, nos interesan las distribuciones marginales de recursos, que estudiamos combinando herramientas analíticas y computacionales. Encontramos que las leyes de potencia persisten en la gran mayoría de las poblaciones interactuantes estudiadas. En los capítulos sucesivos se establecen comparaciones entre las propiedades distintivas de cada modelo, y se discute el rango de validez de las soluciones analíticas obtenidas, que abarcan desde aproximaciones de campo medio a soluciones exactas para sistemas de pocos agentes.
Resumen en inglés
Multiplicative agent systems with stochastic reset are agent-based models (ABM) known for generating stationary power-law probability distributions for individual resources. This property is considered valuable in the literature, given the abundance of power-law distributed variables in various fields such as biology, economics, and linguistics. In this Master's Thesis, we introduce different coupling schemes in the original model, both cooperative and competitive, linear and nonlinear, global and space-extended, and we study the emergent statistical properties of each case. In particular, we are interested in the marginal distributions of resources we obtain by combining analytical and computational tools. We find that power laws persist in the vast majority of the studied populations. In the chapters that follow, we compare the distinctive properties of each model and the range of validity of the analytical solutions obtained, ranging from mean-field approximations to exact solutions for systems with few agents.
| Tipo de objeto: | Tesis (Maestría en Ciencias Físicas) |
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| Palabras Clave: | Chapman-kolmogorov equation; Ecuación de chapman-kolmogorov; [Stochastic resets; Reseteo estocástico Agent based models; Modelo basado en agentes; Power-law; Ley de potencias; Replicator dynamics; Dinámica del replicador; Multiplicative processes; Procesos multiplicativos] |
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| Materias: | Física > Econofísica |
| Divisiones: | Gcia. de área de Investigación y aplicaciones no nucleares > Gcia. de Física > Sistemas complejos y altas energías > Física estadística interdisciplinaria |
| Código ID: | 1057 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 22 Jun 2022 15:49 |
| Última Modificación: | 29 Jun 2022 10:41 |
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