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Integrable Models, Coulomb Interactions, and Mean Field Game Theory
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Integrable Models, Coulomb Interactions, and Mean Field Game Theory. |
| 개인저자 | Cerenzia, Mark. |
| 단체저자명 | Princeton University. Operations Research and Financial Engineering. |
| 발행사항 | [S.l.]: Princeton University., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 111 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-05B. Dissertation Abstract International |
| ISBN | 9781687984647 |
| 학위논문주기 | Thesis (Ph.D.)--Princeton University, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-05, Section: B.
Advisor: Carmona, Rene. |
| 이용제한사항 | This item must not be sold to any third party vendors.This item must not be added to any third party search indexes. |
| 요약 | 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 mathematicsto understand better how such statistics can emerge.One thread pursued some technical aspects from the perspective of the field of IntegrableProbability, which can realize such systems as projections of certain representationtheoretic objects, a connection observed in a non-intersecting Poissonmodel of the entrepreneurial bus system. The other thread focuses on the decentralized manner such statistics canemerge. 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. |
| 일반주제명 | Mathematics. Applied mathematics. Operations research. |
| 언어 | 영어 |
| 바로가기 | 
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