Loop calculus in statistical physics and information science

Michael Chertkov, Vladimir Y. Chernyak

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


Considering a discrete and finite statistical model of a general position we introduce an exact expression for the partition function in terms of a finite series. The leading term in the series is the Bethe-Peierls (belief propagation) (BP) contribution; the rest are expressed as loop contributions on the factor graph and calculated directly using the BP solution. The series unveils a small parameter that often makes the BP approximation so successful. Applications of the loop calculus in statistical physics and information science are discussed.

Original languageEnglish (US)
Article number065102
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
StatePublished - 2006
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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