Award Abstract # 2246683
Exact Formulas for the KPZ Fixed Point and the Directed Landscape

NSF Org: DMS
Division Of Mathematical Sciences
Recipient: UNIVERSITY OF KANSAS CENTER FOR RESEARCH INC
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: FY 2023 = $296,885.00
History of Investigator:
  • Zhipeng Liu (Principal Investigator)
    zhipeng@ku.edu
Recipient Sponsored Research Office: University of Kansas Center for Research Inc
2385 IRVING HILL RD
LAWRENCE
KS  US  66045-7563
(785)864-3441
Sponsor Congressional District: 01
Primary Place of Performance: University of Kansas Center for Research Inc
2385 IRVING HILL RD
Lawrence
KS  US  66045-7552
Primary Place of Performance
Congressional District:
01
Unique Entity Identifier (UEI): SSUJB3GSH8A5
Parent UEI: SSUJB3GSH8A5
NSF Program(s): PROBABILITY
Primary Program Source: 01002324DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 9150
Program Element Code(s): 126300
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.

Please report errors in award information by writing to: awardsearch@nsf.gov.

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