Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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Description:: Interacting particle systems (IPS) are a class of pure jump stochastic processes used to model systems of individual entities, referred to as ``particles", that evolve …
Year:: 2025
Contributor:: Cocomello, Juniper Rosa (creator); Ramanan, Kavita (Advisor); Nguyen, Oanh (Reader); Geman, Stuart (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Stochastic processes; interacting particle systems; local-field equation
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: In this thesis, we explore the behavior of interacting particle systems. The first part of the thesis investigates the long-time behavior of sparsely interacting particles …
Year:: 2025
Contributor:: Hu, Kevin (creator); Ramanan, Kavita (Advisor); Carrillo, Jose A. (Reader); Guillin, Arnaud (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Probability; interacting particle systems; PDE
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: 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 …
Year:: 2014
Contributor:: Wu, Wei (creator); Dupuis, Paul (Director); Ramanan, Kavita (Director); Fleming, Wendell (Reader); Brown University. Applied Mathematics (sponsor)
Genre:: theses
Subject:: interacting particle systems; mean field limits; quasipotential; Large deviations
Language:: English
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: Consider a (possibly non-Markovian) interacting particle system (IPS) indexed by the nodes of a (possibly random) locally finite graph whose vertices and edges are equipped …
Year:: 2022
Contributor:: Ganguly, Ankan (creator); Ramanan, Kavita (Advisor); Geman, Stuart (Reader); Durrett, Rick (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Stochastic processes; Markov random fields; Hydrodynamic limit; local weak convergence; interacting particle systems
Collection:: Applied Mathematics; Theses and Dissertations

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