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Title: Integrable models, Coulomb interactions, and mean field game theory
Authors: Cerenzia, Mark Joseph
Advisors: Carmona, Rene
Contributors: Operations Research and Financial Engineering Department
Keywords: dynamic game theory
mathematical physics
mean field game theory
partial differential equations
random matrix theory
Subjects: Mathematics
Applied mathematics
Operations research
Issue Date: 2019
Publisher: Princeton, NJ : Princeton University
Abstract: Random matrix statistics emerge in a broad class of strongly correlated systems, with evidence suggesting they can play a universal role comparable to the one Gaussian and Poisson distributions do classically. Indeed, studies have identified these statistics among energy levels of heavy nucleii, Riemann zeta zeros, random permutations, and even chicken eyes. But these statistics have also been observed to emerge in decentralized systems, governing the gaps between entrepreneurial buses, parked cars, perched birds, pedestrians, and other forms of traffic. This thesis records two threads the author pursued in an attempt to use rigorous mathematics to understand better how such statistics can emerge. One thread pursued some technical aspects from the perspective of the field of Integrable Probability, which can realize such systems as projections of certain representation theoretic objects, a connection observed in a non-intersecting Poisson model of the entrepreneurial bus system. The other thread focuses on the decentralized manner such statistics can emerge. We accordingly construct certain N player dynamic games on the line and in the plane that admit Coulomb gas dynamics as a Nash equilibrium and investigate their basic features, many of which are atypical or even new for the literature on many player games. Most notably, we find that the universal local limit of the equilibrium is sensitive to the chosen model of player information in one dimension but not in two dimensions.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Operations Research and Financial Engineering

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