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Theory and Applications of Weakly Interacting Markov Processes

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Technical Report,21 Jul 2014,19 Oct 2017

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University of North Carolina - Chapel Hill Chapel Hill United States

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Systems modeled by a large number of dynamic interacting particles have long been of interest in Statistical Physics. In recent years similar models have started appearing in many other fields as well. These include, communication systems e.g. loss network models, random medium access protocols, mathematical finance e.g. mean field games, default clustering in large portfolios, chemical and biological systems e.g. biological aggregation, chemotactic response dynamics, neuroscience and social sciences e.g. opinion dynamics models. The objective of this project is to develop mathematical theory that enables to predict the behavior of the system when the number of particles is very large, with reliable error bounds, particularly when the system is in steady state. The mathematical results that we are interested in take the form of Law of large numbers and Central Limit Theorems.

Subject Categories:

  • Statistics and Probability

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