This graduate-course focuses on the mathematical foundations of stochastic processes with interacting components and some of their manifold applications. The intuitions and rigorous results will be supported by computer simulations and experiments.
https://sites.google.com/view/spin-charm-eu
At the end of the course, the learner will be able to:
1. Formulate common mathematical models of complex interacting systems
2. Apply appropriate mathematical techniques for asymptotic analysis of such models
3. Identify and characterize emergent phenomena and phase transitions
4. Implement simulation algorithms for mathematical models of stochastic processes with interactions
Introductory courses to
1. Probability and Statistics
2. Linear Algebra
3. Calculus
Knowledge about Markov chains and Poisson processes is recommended, but not required.
There is no single textbook for the course, but relevant additional literature and research articles will be made available to students. Course materials, such as lectures notes, video recordings, etc., will also be made available.
* van der Hofstad, Remco. Random graphs and complex networks. Vol. 1. Cambridge university press, 2017.
* Lanchier, Nicolas. Stochastic modeling. Berlin: Springer, 2017.
* Lanchier, Nicolas. Stochastic interacting systems in life and social sciences. Vol. 5. Walter de Gruyter GmbH & Co KG, 2024.
* Roch, Sebastien. Modern discrete probability: An essential toolkit. Cambridge University Press, 2024. https://people.math.wisc.edu/~roch/mdp/
* Conducted online in a hybrid interactive format
* Organized in several modules, each consisting of teaching materials, assignments and quizzes
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