Amarjit Budhiraja
University of North Carolina at Chapel Hill, NC·Mathematics & Statistics
Many real systems are made of huge numbers of parts that constantly affect one another: stocks ranked against each other in a market, jobs routed among thousands of servers in a data center, or agents competing for position. How do such systems settle into stable patterns over time, and how often do they wander far from typical behavior?
- Fields
Mathematics & Statistics
Computer Science
- Topics
interacting particle systems
probability
stochastic processes
- Grants
- 2 known grants, through Jul 2028
What they work on
- Characterize the hydrodynamic limit of the infinite Atlas model, a rank-based particle model from stochastic portfolio theory, by linking it to Stefan-type free boundary problems, especially when particles start densely packed.
- Study the stationary behavior and fluctuation limits of the infinite-dimensional reflected Atlas model that arises from load balancing in large server systems, and connect it to stochastic partial differential equations.
- Develop hydrodynamic limit theory for pure jump processes in which lagging particles move more often, and study their ergodicity, stability and the traveling wave solutions of the associated equations.
- Develop asymptotic theory for large random networks using stochastic analysis, percolation theory and large deviations, alongside optimization and statistical learning approaches to detection and resource allocation on networks.
More about the research
This work builds the probability theory needed to answer those questions for large interacting particle systems and, more broadly, for random networks.
Why it matters
Models of interacting particles describe how cloud computing systems balance load, how stock rankings evolve, and how groups synchronize or compete. Sharper mathematical results on stability and rare deviations could help engineers design large server systems and help analysts understand market dynamics. The network theory and training program prepare students for data-driven work in engineering, business, epidemiology and ecology.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Sandra Cerrai
University of Maryland, MD·Mathematics & Statistics
Prove that the Smoluchowski-Kramers small-mass limit holds for stochastic damped geometric wave equations, starting with one-dimensional stochastic wave maps.
Ludovic Tangpi
Princeton University, NJ·Mathematics & Statistics·Early-career
Develop and analyze a new form of propagation of chaos for interacting particle systems that evolve backward in time, together with the associated functional inequalities, as the main tool for making the mean field game limit rigorous.
Samuel Punshon-Smith
Tulane University of Louisiana, LA·Mathematics & Statistics·Early-career
Develop a microlocal framework, using pseudodifferential operators that track behavior across spatial scales, to analyze how randomly fluctuating velocity fields mix a substance in advection-diffusion and nonlinear fluid PDE models.
The school
University of North Carolina at Chapel Hill: 72 labs on PI Pages, $1.6B a year on research, 523 research doctorates a year.
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