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Multiple Valleys

  • Sourav Chatterjee
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

This chapter gives the formal definition of multiple valleys, and the proof that chaos implies multiple valleys. This is another key result of this monograph. This result is then used to prove multiple valleys in polymer models, spin glasses and the Kauffman-Levin fitness model from evolutionary biology.

References

  1. Chatterjee, S.: Chaos, concentration, and multiple valleys. Preprint (2008b). Available at http://arxiv.org/abs/0810.4221
  2. Chatterjee, S.: Disorder chaos and multiple valleys in spin glasses. Preprint (2009). Available at http://arxiv.org/abs/0907.3381
  3. Durrett, R., Limic, V.: Rigorous results for the NK model. Ann. Probab. 31(4), 1713–1753 (2003) CrossRefzbMATHMathSciNetGoogle Scholar
  4. Evans, S.N., Steinsaltz, D.: Estimating some features of NK fitness landscapes. Ann. Appl. Probab. 12(4), 1299–1321 (2002) CrossRefzbMATHMathSciNetGoogle Scholar
  5. Kauffman, S.A., Levin, S.A.: Towards a general theory of adaptive walks on rugged landscapes. J. Theor. Biol. 128, 11–45 (1987) CrossRefMathSciNetGoogle Scholar
  6. Limic, V., Pemantle, R.: More rigorous results on the Kauffman-Levin model of evolution. Ann. Probab. 32(3A), 2149–2178 (2004) CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sourav Chatterjee
    • 1
  1. 1.Department of StatisticsStanford UniversityStanfordUSA

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