Loop Calculus in Statistical Physics and Information Science

Details Loop Calculus in Statistical Physics and Information Science Loop Calculus in Statistical Physics and Information Science

2006-01-20

arxiv.org/abs/cond-mat/0601487v2

Phys. Rev. E 73, 065102(R) (2006)

Physics

Condensed Matter

Statistical Mechanics

4 pages, submitted to Phys.Rev.Lett. Changes: More general model, Simpler derivation

Scientific paper

10.1103/PhysRevE.73.065102

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.

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