LEADER 03083nam a2200481 i 4500 001 991003392369707536 006 m o d 007 cr |n||||||||| 008 170629s2017 sz ob 001 0 eng d 020 $a9783319504872$q(electronic bk.) 035 $ab14326930-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a519.282$223 084 $aAMS 60K37 084 $aAMS 60F10 084 $aAMS 60H05 084 $aAMS 60J10 084 $aAMS 82-01 084 $aAMS 82B20 084 $aAMS 82B41 084 $aAMS 82D60 084 $aLC QA274.73 100 1 $aComets, Francis$0739978 245 10$aDirected polymers in random environments$h[e-book] :$bÉcole d'Été de Probabilités de Saint-Flour XLVI-2016 /$cFrancis Comets 260 $aCham :$bSpringer,$c2017 300 $a1 online resource 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture notes in mathematics,$x1617-9692 ;$v2175 504 $aIncludes bibliographical references and index 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 $aAnalyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main question is: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed? This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students 650 0$aRandom walks (Mathematics) 650 0$aMartingales (Mathematics) 711 2 $aEcole d'été de probabilités de Saint-Flour$n<46. ;$d2016 ;$cSaint-Flour, France> 776 08$aPrint version:$z9783319504865 856 40$uhttps://link.springer.com/book/10.1007/978-3-319-50487-2$zAn electronic book accessible through the World Wide Web 907 $a.b14326930$b03-03-22$c29-06-17 912 $a991003392369707536 996 $aDirected polymers in random environments$91466418 997 $aUNISALENTO 998 $ale013$b29-06-17$cm$d@ $e-$feng$gsz $h0$i0 LEADER 00938nam a2200253 i 4500 001 991002688869707536 005 20020508204344.0 008 960614s1983 it ||| | ita 020 $a8870264548 035 $ab1104584x-39ule_inst 035 $aPARLA167173$9ExL 040 $aDip.to scienze storiche$bita 100 1 $aCaroli, Ernesto$0211129 245 10$aDizionario francescano :$bSpiritualita /$c[coordinatore generale Ernesto Caroli] 260 $aPadova :$bEdizioni messaggero,$c1983 300 $aXXII, 2374 p. ;$c21 cm. 650 4$aFrancescanesimo - Lessicografia 650 4$aSpiritualità - Lessicografia 907 $a.b1104584x$b02-04-14$c28-06-02 912 $a991002688869707536 945 $aLE009 STOR. 40.1-4$g1$i2009000095694$lle009$o-$pE0.00$q-$rl$s- $t0$u0$v0$w0$x0$y.i11169953$z28-06-02 996 $aDizionario francescano$9858925 997 $aUNISALENTO 998 $ale009$b01-01-96$cm$da $e-$fita$git $h0$i1