- Title Information
- Title
- Non-Markovian Interacting Particle Systems on Large Sparse Graphs: Hydrodynamic Limits and Marginal Characterizations
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Ganguly, Ankan
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Ramanan, Kavita
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Geman, Stuart
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Durrett, Rick
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2022
- Physical Description
- Extent
- xi, 208 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2022
- Genre (aat)
- theses
- Abstract
- 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 with marks representing parameters of the model such as the environment and initial conditions. Each particle takes values in a countable state space and evolves according to a pure jump process whose jump intensities depend only on its own history and marks as well as the histories and marks of particles and edges in its neighborhood. Under mild conditions, we establish the well-posedness of IPS on a large class of locally finite graphs, and we provide an explicit example in which well-posedness fails. We additionally prove that under suitably mild conditions, the trajectories of the IPS are continuous with respect to their initial conditions in three different respects, one of which is novel and another of which directly implies the convergence of multiple hydrodynamic limits. It is well-known that the majority of sparse graph sequences of interest in the literature converge to trees, so we next address the problem of characterizing the marginal distribution of an IPS on a regular tree (an infinite tree of homogeneous degree). We derive an autonomous, non-Markovian, non-linear SDE called the local equation, and we prove that, for sufficiently symmetric initial conditions, the local equation is well-posed and the law of its solutions is equal to the marginal law of the IPS. This extends recent work that proved similar results for interacting diffusions with i.i.d. initial conditions. Our extension allows us to investigate flow and stationary properties of solutions to the local equation. We finish by deriving a Markovian approximation to the local equation, proving that it exactly captures stationary solutions to certain reversible IPS and present numerical examples demonstrating the efficacy of this approximation to different IPS.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01133519")
- Topic
- Stochastic processes
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01010351")
- Topic
- Markov random fields
- Subject
- Topic
- Hydrodynamic limit
- Subject
- Topic
- local weak convergence
- Subject
- Topic
- interacting particle systems
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20221018