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Phase Transitions in Discrete Structures

  • Amin Coja-OghlanEmail author
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2144)

Abstract

Over the past 20 years physicists have developed an ingenious but non-rigorous approach to random discrete structures, the so-called cavity method. This technique has led to many intriguing predictions as to, e.g., the precise location and nature of phase transitions and the performance of algorithms. In these notes I give a brief survey of the cavity method as well as an introduction into recent mathematical research aiming at putting the cavity method on a rigorous foundation.

Keywords

Partition Function Belief Propagation Boltzmann Distribution Function Node Variable Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I am grateful to Victor Bapst for his comments on a draft version of these notes.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Mathematics InstituteGoethe UniversityFrankfurtGermany

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