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020 _a9783642211560
_9978-3-642-21156-0
024 7 _a10.1007/978-3-642-21156-0
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aGiacomin, Giambattista.
_eauthor.
245 1 0 _aDisorder and Critical Phenomena Through Basic Probability Models
_h[electronic resource] :
_bÉcole d’Été de Probabilités de Saint-Flour XL – 2010 /
_cby Giambattista Giacomin.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _aXI, 130p. 12 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2025
505 0 _a1 Introduction -- 2 Homogeneous pinning systems: a class of exactly solved models -- 3 Introduction to disordered pinning models -- 4 Irrelevant disorder estimates -- 5 Relevant disorder estimates: the smoothing phenomenon -- 6 Critical point shift: the fractional moment method -- 7 The coarse graining procedure -- 8 Path properties.
520 _aUnderstanding the effect of disorder on critical phenomena is a central issue in statistical mechanics. In probabilistic terms: what happens if we perturb a system exhibiting a phase transition by introducing a random environment? The physics community has approached this very broad question by aiming at general criteria that tell whether or not the addition of disorder changes the critical properties of a model: some of the predictions are truly striking and mathematically challenging. We approach this domain of ideas by focusing on a specific class of models, the "pinning models," for which a series of recent mathematical works has essentially put all the main predictions of the physics community on firm footing; in some cases, mathematicians have even gone beyond, settling a number of controversial issues. But the purpose of these notes, beyond treating the pinning models in full detail, is also to convey the gist, or at least the flavor, of the "overall picture," which is, in many respects, unfamiliar territory for mathematicians.
650 0 _aMathematics.
650 0 _aDistribution (Probability theory).
650 0 _aMathematical physics.
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aApplications of Mathematics.
650 2 4 _aStatistical Physics, Dynamical Systems and Complexity.
650 2 4 _aMathematical Methods in Physics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642211553
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2025
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-21156-0
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c107914
_d107914