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020 _a9783319504872
_9978-3-319-50487-2
024 7 _a10.1007/978-3-319-50487-2
_2doi
040 _aISI Library, Kolkata
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
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072 7 _aMAT029000
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072 7 _aPBT
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082 0 4 _a519.2
_223
100 1 _aComets, Francis.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aDirected Polymers in Random Environments
_h[electronic resource] :
_bÉcole d'Été de Probabilités de Saint-Flour XLVI – 2016 /
_cby Francis Comets.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXVI, 199 p. 20 illus., 2 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_v2175
505 0 _a1 Introduction -- 2 Thermodynamics and Phase Transition -- 3 The martingale approach and the L2 region -- 4 Lattice versus tree -- 5 Semimartingale approach and localization transition -- 6 Log-Gamma polymer model -- 7 Kardar-Parisi-Zhang equation and universality -- 8 Variational formulas.
520 _aAnalyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main question is: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed? This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.
650 0 _aDistribution (Probability theory.
650 0 _aStatistical physics.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aStatistical Physics and Dynamical Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P19090
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319504865
776 0 8 _iPrinted edition:
_z9783319504889
830 0 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_v2175
856 4 0 _uhttps://doi.org/10.1007/978-3-319-50487-2
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c427245
_d427245