LEADER 04371nam 22005775 450 001 9910155270403321 005 20250610110142.0 010 $a3-319-49499-6 024 7 $a10.1007/978-3-319-49499-9 035 $a(CKB)3710000000974375 035 $a(DE-He213)978-3-319-49499-9 035 $a(MiAaPQ)EBC4771598 035 $a(PPN)197456766 035 $a(MiAaPQ)EBC29091020 035 $a(EXLCZ)993710000000974375 100 $a20161218d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aReflected Brownian motions in the KPZ universality class /$fby Thomas Weiss, Patrik Ferrari, Herbert Spohn 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (VII, 118 p. 4 illus.) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v18 311 08$a3-319-49498-8 320 $aIncludes bibliographical references. 327 $aIntroduction -- One-sided reflected Brownian motions and related models -- Skorokhod construction -- Packed initial conditions -- Infinite particle systems -- Determinantal point processes -- Definition -- Fredholm determinants -- Correlation kernel -- Strategy for future proofs.-Airy processes.-Elementary Airy processes -- Crossover Processes -- Variational identities -- Gaussian fluctuations of the Airy_stat process -- Packed and Periodic initial conditions -- Packed initial conditions -- Periodic initial conditions -- Stationary initial conditions -- Poisson initial conditions -- Determinantal structure -- Asymptotic analysis -- Path-integral style formula -- Analytic continuation -- More general initial conditions and their asymptotics -- Half-Periodic initial conditions -- Half-Poisson initial conditions -- Poisson-Periodic initial conditions -- Attractiveness and a more general class of initial data -- Asymptotics along space-like paths and slow decorrelations -- References. 330 $aThis book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions (Chapter 5), stationary initial conditions (Chapter 6), and mixtures thereof (Chapter 7). The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. These notes serve as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. The notes will be of interest to readers from interacting diffusion processes and non-equilibrium statistical mechanics. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v18 606 $aStatistical physics 606 $aMathematical physics 606 $aProbabilities 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aStatistical physics. 615 0$aMathematical physics. 615 0$aProbabilities. 615 14$aStatistical Physics and Dynamical Systems. 615 24$aMathematical Physics. 615 24$aProbability Theory and Stochastic Processes. 676 $a530 700 $aWeiss$b Thomas$4aut$4http://id.loc.gov/vocabulary/relators/aut$0823916 702 $aFerrari$b Patrik$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSpohn$b Herbert$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910155270403321 996 $aReflected Brownian Motions in the KPZ Universality Class$92275362 997 $aUNINA