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1. Wu, Wei. Large deviations and quasipotential for finite state mean field interacting particle systems.

Degree: PhD, Applied Mathematics, 2014, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:386248/

We study a general class of mean field interacting
particle systems with a finite state space. Particles evolve as
exchangeable jump Markov processes, where finite collections of
particles are allowed to change their state simultaneously. Such
models arise naturally in statistical physics, queueing systems and
communication networks literatures. In the first part of the
thesis, we establish a large deviation principle for the empirical
measure process for the interacting particle systems. The approach
is based on a variational representation for functionals of a
Poisson random measure. Under an appropriate communication
condition, we also prove a locally uniform large deviation
principle. The main novelty is that more than one particle is
allowed to change its state simultaneously, and so a standard
approach to the proof based on change of measure is not possible.
Along the way, we establish an LDP for jump Markov processes on the
simplex, whose rates decay to zero as they approach the boundary of
the domain. This result may be of independent interest. In the
second part of the thesis, we focus on the mean field interacting
particle systems that only admit single particle jumps. Under the
assumption that there exists a unique stationary measure, we
construct a Markov chain approximation of the quasipotential
function associated with the equilibrium. This is the first example
of the Markov chain approximation for problems with non-quadratic
running cost (but still convex in the control), which may also have
singularities near the boundary.
*Advisors/Committee Members: Dupuis, Paul (Director), Ramanan, Kavita (Director), Fleming, Wendell (Reader).*

Subjects/Keywords: interacting particle systems

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APA (6^{th} Edition):

Wu, W. (2014). Large deviations and quasipotential for finite state mean field interacting particle systems. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:386248/

Chicago Manual of Style (16^{th} Edition):

Wu, Wei. “Large deviations and quasipotential for finite state mean field interacting particle systems.” 2014. Doctoral Dissertation, Brown University. Accessed October 20, 2020. https://repository.library.brown.edu/studio/item/bdr:386248/.

MLA Handbook (7^{th} Edition):

Wu, Wei. “Large deviations and quasipotential for finite state mean field interacting particle systems.” 2014. Web. 20 Oct 2020.

Vancouver:

Wu W. Large deviations and quasipotential for finite state mean field interacting particle systems. [Internet] [Doctoral dissertation]. Brown University; 2014. [cited 2020 Oct 20]. Available from: https://repository.library.brown.edu/studio/item/bdr:386248/.

Council of Science Editors:

Wu W. Large deviations and quasipotential for finite state mean field interacting particle systems. [Doctoral Dissertation]. Brown University; 2014. Available from: https://repository.library.brown.edu/studio/item/bdr:386248/