
NSF Org: |
DMS Division Of Mathematical Sciences |
Recipient: |
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Initial Amendment Date: | March 28, 2023 |
Latest Amendment Date: | March 28, 2023 |
Award Number: | 2246683 |
Award Instrument: | Standard Grant |
Program Manager: |
Tomek Bartoszynski
tbartosz@nsf.gov (703)292-4885 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
Start Date: | July 1, 2023 |
End Date: | June 30, 2026 (Estimated) |
Total Intended Award Amount: | $296,885.00 |
Total Awarded Amount to Date: | $296,885.00 |
Funds Obligated to Date: |
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History of Investigator: |
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Recipient Sponsored Research Office: |
2385 IRVING HILL RD LAWRENCE KS US 66045-7563 (785)864-3441 |
Sponsor Congressional District: |
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Primary Place of Performance: |
2385 IRVING HILL RD Lawrence KS US 66045-7552 |
Primary Place of
Performance Congressional District: |
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Unique Entity Identifier (UEI): |
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Parent UEI: |
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NSF Program(s): | PROBABILITY |
Primary Program Source: |
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Program Reference Code(s): |
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Program Element Code(s): |
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Award Agency Code: | 4900 |
Fund Agency Code: | 4900 |
Assistance Listing Number(s): | 47.049 |
ABSTRACT
The project aims to study the properties of limiting random fields arising from a broad class of physical and probabilistic models, including random growing interfaces, interacting particle systems, and polymers in random environments. This class is called the Kardar-Parisi-Zhang universality class, and it models many real-world phenomena, such as fire propagation, traffic flow, or disordered polymer chains. It has been conjectured and partially proved that all models in the Kardar-Parisi-Zhang universality class exhibit the same limiting behaviors. Understanding these behaviors has become an important area in probability theory and more generally in mathematics. The awardee mentors graduate and undergraduate students and is engaged in educational outreach.
The height functions of models in the Kardar-Parisi-Zhang universality class are expected to converge to a limiting space-time fluctuation field, which is called the KPZ fixed point. Moreover, there is a random directed metric on the space-time plane that is expected to govern all the models in the Kardar-Parisi-Zhang universality class. This directed metric is called the directed landscape. While both the KPZ fixed point and the directed landscape are central to the study of the Kardar-Parisi-Zhang universality class, they have only been characterized very recently. The project aims to study these random fields using the approach of exact formulas. The research will first focus on finding exact formulas for the limiting fields in certain exactly solvable models in the Kardar-Parisi-Zhang universality class, such as the directed last passage percolation; these formulas can be used to understand probabilistic properties of the limiting fields. A second goal of this project is to extend the approaches described above to periodic domains.
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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