Stochastic spatial models of social dynamics Project Summary Nicolas Lanchier The development and analysis of mathematical models in general and stochastic processes in particular have had a tremendous impact in the advance of physical sciences and more recently life sciences, often leading to predictions that were unexpected based on experimental studies. The use of stochastic models in the rapidly growing field of social sciences is equally important, driving the leading social scientists to develop a number of stochastic models of social dynamics to understand complex systems at the population level. The recent development of these models has resulted in the formulation of conjectures still unexplored by researchers in the field of probability theory and stochastic processes. Motivated by the need for analytical results in social sciences, the main objective of this proposal is to prove (or disprove) important conjectures for some of the most popular models of social dynamics and new results for natural variants of these models. Intellectual Merit. The primary objective of this research program is to conduct a thorough mathematical analysis of some of the most popular models of social dynamics that fall in the framework of agent-based models also called interacting particle systems. These models have been intensively used by social scientists and cover a number of branches of social sciences: opinion dynamics, cultural dynamics, language dynamics and evolutionary game dynamics. Even though a number of conjectures are available, the rigorous mathematical analysis of these models remains necessary as suggested by preliminary works of the PI as well as results anticipated in this proposal that contradict some of these conjectures, leading to conclusions that numerical simulations and heuristic arguments have failed to predict. In view of the lack of analytical results for stochastic spatial models of social dynamics and therefore the novelty of this topic, such a research project requires the development of new mathematical tools, which includes new geometrical arguments, new coupling arguments and new duality techniques. In particular, in addition to being a key step for the understanding of social dynamics, this research program also constitutes an important contribution to the field of interacting particle systems. In short, this is a proposal highly motivated by social sciences but with an accomplishment in mathematics and an impact in both fields. Broader Impacts. Because this proposal gives rigorous answers to some of the most important questions asked by the leading social scientists, its impact is obviously not limited to the field of stochastic processes: it represents a key step for the advance of social sciences and our understanding of social dynamics of populations. In particular, the PI will pursue his effort to build a bridge between mathematics and social sciences by making the mathematical findings resulting from this research program available to social scientists in the form of oral presentations at local seminars and conferences across the US. The inter-disciplinarily of our proposed research is also important in terms of educational perspectives by promoting the involvement of students at different levels and with different backgrounds and interests. In particular, the PI is currently supervising one graduate student on the topic of evolutionary game dynamics for his Doctoral Dissertation and has recently supervised six undergraduate students for their Honors Theses: three on the topic of evolutionary game dynamics, two on the topic of opinion dynamics that both resulted in a research paper, and one on the topic of cultural dynamics. The graduate level stochastic modeling class designed by the PI has also been recently completed to include lectures on some of the preliminary works on cultural dynamics and evolutionary game dynamics, which shows the potential of this research in terms of curriculum development. As a regular speaker at the summer program of the Mathematical and Theoretical Biology Institute, the PI will also have the opportunity to present the work resulting from this research every year to underrepresented minorities.
|Effective start/end date||3/24/15 → 9/24/17|
- DOD: National Security Agency (NSA): $39,909.00
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