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Research Spending & Results

Award Detail

Awardee:CARNEGIE MELLON UNIVERSITY
Doing Business As Name:Carnegie-Mellon University
PD/PI:
  • Wesley Pegden
  • (412) 268-9527
  • wes@math.cmu.edu
Award Date:06/22/2021
Estimated Total Award Amount: $ 210,000
Funds Obligated to Date: $ 210,000
  • FY 2021=$210,000
Start Date:06/01/2021
End Date:05/31/2024
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Discrete Random and Pseudorandom Structures
Federal Award ID Number:2054503
DUNS ID:052184116
Parent DUNS ID:052184116
Program:Combinatorics
Program Officer:
  • Tomek Bartoszynski
  • (703) 292-4885
  • tbartosz@nsf.gov

Awardee Location

Street:5000 Forbes Avenue
City:PITTSBURGH
State:PA
ZIP:15213-3815
County:Pittsburgh
Country:US
Awardee Cong. District:18

Primary Place of Performance

Organization Name:Carnegie-Mellon University
Street:5000 Forbes Avenue
City:PITTSBURGH
State:PA
ZIP:15213-3815
County:Pittsburgh
Country:US
Cong. District:18

Abstract at Time of Award

This project aims to better understand random and pseudorandom processes, and the interplay between them. In particular, the project studies models from statistical physics of aggregation processes built on both random and pseudorandom walks. For example, in the former case, diffusion limited aggregation processes produce intricate fractals through processes analogous to those that drive the formation of corals, but the propensity of these processes to give rise to long, spiny, structures is still not rigorously understood. In the latter case, the Abelian sandpile process builds a cluster of particles through a pseudorandom distribution of particles that ends up giving rise to intricate fractal patterns, as well as statistical laws which reappear throughout nature (e.g., as the frequency distributions of earthquakes, avalanches, etc). Among other goals, this project aims to better understand the dependence of the behavior of the Abelian sandpile on the underlying lattice. One particularly interesting case is that where a periodic lattice is subjected to random edge-deletions; in this case the Abelian sandpile is a pseudorandom aggregation process on a random environment, which we expect to behave like a random aggregation process on a periodic environment. Other topics include work on Euclidean functionals; in particular, refining our understanding of asymptotic relationships between structures like Traveling Salesperson Tours through typical (i.e. random) point sets, and their algorithmic approximations. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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