Everything about Partition function (mathematics)
Generalization of the concept from statistical mechanics
The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution. The partition function occurs in many problems of probability theory because, in situations where there is a natural symmetry, its associated probability measure, the Gibbs measure, has the Markov property. This means that the partition function occurs not only in physical systems with translation symmetry, but also in such varied settings as neural networks, and applications such as genomics, corpus linguistics and artificial intelligence, which employ Markov networks, and Markov logic networks. The Gibbs measure is also the unique measure that has the property of maximizing the entropy for a fixed expectation value of the energy; this underlies the appearance of the partition function in maximum entropy methods and the algorithms derived therefrom. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Partition function (mathematics)A 5-minute orientation
- Pick up a classic book: Über Modulfunktionen und PartitionenproblemeThe most-reprinted book on the subject
- Read the landmark paper: A paradox in the electronic partition function or how to be cautious with mathematicsCited 3 times
- Go sideways: Bernoulli schemeA closely related topic
- Go sideways: Mutual informationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
📚 Books worth reading
- 📕Über Modulfunktionen und PartitionenproblemeHans Petersson · 1954
Ramanujan's forty identities for the Rogers-Ramanujan functionsBruce C. Berndt, Geumlan Choi · 2007- 📕A partition function with the prime modulus P>3John Livingood · 1945
Partitions, q-Series, and Modular FormsKrishnaswami Alladi · 2012- 📕Structures of subpartitions related to a submodular function minimizationTakeshi Naitoh, Akira Nakayama · 1995
Path functions and generalized basic hypergeometric functionsKevin W. J. Kadell · 1987
Analytic and combinatorial generalizations of the Rogers-Ramanujan identitiesDavid M. Bressoud · 1980
Path functions and generalized basic hypergeometric functionsKevin W. J. Kadell · 1987
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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