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Statistical Physics Concepts & Tools for Complex Systems
In this course, you will learn tools and ideas developed by statistical physics to deal with "complex systems". These tools can be used in different contexts, including economics and social sciences where the modelling of collective phenomena, crises, panics, and discontinuities, is more necessary than ever.
Evaluation
The written exam will be based on a recent article. The exam will consist in two parts, a first technical part related to the calculation exposed in the article, and a second interpretation part to assess your understanding of the article's implications and broader context.
Syllabus
- General Introduction & Scope of the lectures
- Mild fluctuations vs. Wild fluctuations
- Introduction: Thin tails/Fat tails, scale invariance
- The « problem » with power-laws: concentration/localisation, generalised CLT
- Scenarii for power-laws, universality?
- Multiplicative growth models for population
- Uncorrelated growth, log-normal fluctuations
- Sums of log-normals & condensation
- Growth with redistribution/mixing
- Continuous limit & the Hamilton-Jacobi-Bellman method
- Networks
- Erdos-Renyi networks, percolation, branching process
- Growing networks, scale-free networks
- Resilience, breakdown, epidemics
- Firm Networks
- Interactions, instabilities & collective effects
- The Curie-Weiss paradigm: self-fulfilling prophecies, hysteresis
- The Random Ising Field Model paradigm: crises & sudden opinion shifts
- Optimisation vs. Resilience
- Temporal criticality: synchronization, failures
- Random Matrices
- Introduction
- The Wigner Semi-Circle
- Dyson Brownian motion & Free Random Matrices
- Random Covariance Matrices
- Network Matrices & Economic Stability
Prerequisites
Taste for modelling, probabilities and statistics.
Evaluation
The written exam will be based on a recent article. The exam will consist in two parts, a first technical part related to the calculation exposed in the article, and a second interpretation part to assess your understanding of the article's implications and broader context.