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Information, Physics, and Computation$
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Marc Mézard and Andrea Montanari

Print publication date: 2009

Print ISBN-13: 9780198570837

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780198570837.001.0001

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An ongoing story

An ongoing story

(p.517) 22 An ongoing story
Information, Physics, and Computation

Marc Mézard

Andrea Montanari

Oxford University Press

The emerging field that has been described in this book is remarkably coherent, but it also opens up a number of challenges. This chapter provides a synthetic description of such challenges, as well as a survey of recent progress. The ambition is to set an agenda for this new research field. Three research directions are emphasized. Firstly, achieving a better qualitative understanding of 1RSB glass phase. What is a pure state decomposition? What is the relation between emergence of long range correlations and clustering of the probability measure? Secondly, developing methods for the full-RSB phase. Where does such a phase emerge in sparse graphical models? Does the cavity method have a compact formulation? Thirdly, understanding algorithmic implications. There is large evidence that phase transitions affect the performances of algorithms. However, a crisp and general formulation is still missing.

Keywords:   phase transition, glass, replica symmetry breaking, cluster, pure state, correlation

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