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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

Chapter:
(p.517) 22 An ongoing story
Source:
Information, Physics, and Computation
Author(s):

Marc Mézard

Andrea Montanari

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198570837.003.0022

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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