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001 978-3-7643-9891-0
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005 20181204133146.0
007 cr nn 008mamaa
008 100301s2009 sz | s |||| 0|eng d
020 _a9783764398910
_9978-3-7643-9891-0
024 7 _a10.1007/978-3-7643-9891-0
_2doi
040 _aISI Library, Kolkata
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
245 1 0 _aSpin Glasses: Statics and Dynamics
_h[electronic resource] :
_bSummer School, Paris 2007 /
_cedited by Anne Boutet de Monvel, Anton Bovier.
264 1 _aBasel :
_bBirkhäuser Basel,
_c2009.
300 _aXII, 278 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Probability,
_x1050-6977 ;
_v62
505 0 _aMean Field -- A Short Course on Mean Field Spin Glasses -- REM Universality for Random Hamiltonians -- Another View on Aging in the REM -- Spin Glass Identities and the Nishimori Line -- Self-averaging Identities for Random Spin Systems -- Chaos in Mean-field Spin-glass Models -- A non Gaussian Limit Law for the Covariances of Spins in a SK Model with an External Field -- A Limit Theorem for Mean Magnetisation in the Sherrington-Kirkpatrick Model with an External Field -- Non-mean Field -- A Percolation-theoretic Approach to Spin Glass Phase Transitions -- Fluctuations in Finite-dimensional Spin-glass Dynamics -- Disordered Pinning Models -- Renewal Sequences, Disordered Potentials, and Pinning Phenomena -- A Smoothing Inequality for Hierarchical Pinning Models.
520 _aOver the last decade, spin glass theory has turned from a fascinating part of t- oretical physics to a ?ourishing and rapidly growing subject of probability theory as well. These developments have been triggered to a large part by the mathem- ical understanding gained on the fascinating and previously mysterious “Parisi solution” of the Sherrington–Kirkpatrick mean ?eld model of spin glasses, due to the work of Guerra, Talagrand, and others. At the same time, new aspects and applications of the methods developed there have come up. The presentvolumecollects a number of reviewsaswellas shorterarticlesby lecturers at a summer school on spin glasses that was held in July 2007 in Paris. These articles range from pedagogical introductions to state of the art papers, covering the latest developments. In their whole, they give a nice overview on the current state of the ?eld from the mathematical side. The review by Bovier and Kurkova gives a concise introduction to mean ?eld models, starting with the Curie–Weiss model and moving over the Random Energymodels up to the Parisisolutionof the Sherrington–Kirkpatrikmodel. Ben Arous and Kuptsov present a more recent view and disordered systems through the so-called local energy statistics. They emphasize that there are many ways to look at Hamiltonians of disordered systems that make appear the Random Energy model (or independent random variables) as a universal mechanism for describing certain rare events. An important tool in the analysis of spin glasses are correlation identities.
650 0 _aDistribution (Probability theory.
650 0 _aMathematical physics.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
700 1 _aMonvel, Anne Boutet de.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aBovier, Anton.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783764399153
776 0 8 _iPrinted edition:
_z9783764389994
830 0 _aProgress in Probability,
_x1050-6977 ;
_v62
856 4 0 _uhttps://doi.org/10.1007/978-3-7643-9891-0
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c426164
_d426164