LEADER 04987nam 22006255 450 001 9910300244403321 005 20200702041156.0 010 $a3-319-24777-8 024 7 $a10.1007/978-3-319-24777-9 035 $a(CKB)3710000000596638 035 $a(EBL)4405863 035 $a(SSID)ssj0001654092 035 $a(PQKBManifestationID)16433178 035 $a(PQKBTitleCode)TC0001654092 035 $a(PQKBWorkID)14982352 035 $a(PQKB)10044823 035 $a(DE-He213)978-3-319-24777-9 035 $a(MiAaPQ)EBC4405863 035 $z(PPN)258851422 035 $a(PPN)19220226X 035 $a(EXLCZ)993710000000596638 100 $a20160211d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMetastability $eA Potential-Theoretic Approach /$fby Anton Bovier, Frank den Hollander 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (578 p.) 225 1 $aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v351 300 $aDescription based upon print version of record. 311 $a3-319-24775-1 320 $aIncludes bibliographical references and index. 327 $aPart I Introduction -- 1.Background and motivation -- 2.Aims and scopes -- Part II Markov processes 3.Some basic notions from probability theory -- 4.Markov processes in discrete time -- 5.Markov processes in continuous time -- 6.Large deviations -- 7.Potential theory -- Part III Metastability -- 8.Key definitions and basic properties -- 9.Basic techniques -- Part IV Applications: Diffusions with small noise -- 10.Discrete reversible diffusions -- 11.Diffusion processes with gradient drift -- 12.Stochastic partial differential equations -- Part V Applications: Coarse-graining at positive temperatures -- 13.The Curie-Weiss model -- 14.The Curie-Weiss model with a random magnetic field: discrete distributions -- 15.The Curie-Weiss model with random magnetic field: continuous distributions -- Part VI Applications: Lattice systems in small volumes at low temperatures -- 16.Abstract set-up and metastability in the zero-temperature limit -- 17.Glauber dynamics -- 18.Kawasaki dynamics -- Part VII Applications: Lattice systems in large volumes at low temperatures -- 19.Glauber dynamics -- 20.Kawasaki dynamics -- Part VIII Applications: Lattice systems in small volumes at high densities -- 21.The zero-range process -- Part IX Challenges -- 22.Challenges within metastability -- 23.Challenges beyond metastability -- References.-Glossary -- Index. . 330 $aMetastability is a wide-spread phenomenon in the dynamics of non-linear systems - physical, chemical, biological or economic - subject to the action of temporal random forces typically referred to as noise. This monograph provides a concise presentation of mathematical approach to metastability based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focus on the precise analysis of the respective hitting probabilities and hitting times of these sets. The theory is illustrated with many examples, ranging from finite-state Markov chains, finite-dimensional diffusions and stochastic partial differential equations, via mean-field dynamics with and without disorder, to stochastic spin-flip and particle-hopping dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability. 410 0$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v351 606 $aProbabilities 606 $aMathematical physics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 615 0$aProbabilities. 615 0$aMathematical physics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aMathematical Physics. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a510 700 $aBovier$b Anton$4aut$4http://id.loc.gov/vocabulary/relators/aut$0300719 702 $aden Hollander$b Frank$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300244403321 996 $aMetastability$92533501 997 $aUNINA