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Opportunity Summary:

The National Science Foundation (NSF) Probability Program (Funding Opportunity Number PD 04 1263, titled "Probability") is a discretionary grant opportunity within NSF's Mathematical and Physical Sciences portfolio (CFDA 47.049). Its purpose is to fund research that advances both the theoretical foundations of probability and its practical uses across a wide range of scientific and engineering contexts. The program is centered on supporting high-quality, original research projects that develop new probabilistic methods, strengthen core theory, and deepen understanding of random phenomena that appear in mathematics and in real-world systems.

The scope of research areas covered by this program is broad and reflects many of the major pillars of modern probability. It explicitly includes discrete probability (covering probabilistic methods in combinatorics, random graphs, and randomized structures), stochastic processes (the study of time-evolving random systems), limit theory (laws of large numbers, central limit behavior, large deviations, and related asymptotics), interacting particle systems (models of many-component random dynamics with interaction, often connected to statistical physics and network behavior), stochastic differential equations and stochastic partial differential equations (continuous-time models driven by noise, relevant to physics, finance, biology, and engineering), and Markov processes (random processes with a memoryless property, including chains and continuous-state variants). While these topics are named directly, the program description is written broadly enough to accommodate closely related probability research that fits the same intellectual mission.

A key emphasis of the opportunity is encouraging probability research that connects to other disciplines. Projects that demonstrate strong applications to areas of science and engineering are described as "especially encouraged." In practice, this can include probabilistic modeling, analysis, and theory development motivated by problems in fields such as statistical physics, computer science and algorithms, communications and information theory, machine learning and data-driven modeling, operations research, epidemiology, quantitative biology, climate and geophysical modeling, materials science, and financial mathematics. The underlying message is that NSF is interested not only in probability as a self-contained branch of mathematics, but also in probability as a language and toolkit for addressing complex systems where uncertainty, randomness, or noise are central features.

In terms of administrative details, the opportunity is listed as a grant funding instrument and indicates no cost sharing or matching requirement. Eligibility is described as "unrestricted," meaning it is broadly open to applicants (subject to any clarifications that would normally appear in the full program announcement text). The opportunity was originally posted March 4, 2009, with an original full proposal window of October 23, 2009 through November 7, 2009, and it notes that the window occurred annually thereafter. The record also shows that this specific listing was later replaced by PD 10 1263 and archived on September 7, 2010, which means applicants would need to consult the successor program description for current deadlines and submission instructions. The listing reports "ExpectedAwards: 0" and "EstimatedTotalFunding: 0," which commonly indicates that award counts and totals were not populated in this particular archived grants.gov entry rather than implying the program made no awards.

For practical access and support, the entry points applicants to the NSF Program Description (04 1263) as the additional information link and provides a contact pathway for technical issues: if there are problems accessing the announcement through grants.gov, applicants are directed to NSF grants.gov support at grantsgovsupport@nsf.gov. Since the entry is archived and replaced, the most reliable path for anyone planning to apply is to locate the current NSF Probability Program solicitation or program page, confirm the active funding opportunity number, and follow the current submission windows and proposal preparation guidance.

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