03083nam a2200481 i 4500991003392369707536m o d cr |n|||||||||170629s2017 sz ob 001 0 eng d9783319504872(electronic bk.)b14326930-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng519.28223AMS 60K37AMS 60F10AMS 60H05AMS 60J10AMS 82-01AMS 82B20AMS 82B41AMS 82D60LC QA274.73Comets, Francis739978Directed polymers in random environments[e-book] :École d'Été de Probabilités de Saint-Flour XLVI-2016 /Francis CometsCham :Springer,20171 online resourcetexttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture notes in mathematics,1617-9692 ;2175Includes bibliographical references and index1 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.Analyzing 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. studentsRandom walks (Mathematics)Martingales (Mathematics)Ecole d'été de probabilités de Saint-Flour<46. ;2016 ;Saint-Flour, France>Print version:9783319504865https://link.springer.com/book/10.1007/978-3-319-50487-2An electronic book accessible through the World Wide Web.b1432693003-03-2229-06-17991003392369707536Directed polymers in random environments1466418UNISALENTOle01329-06-17m@ -engsz 00