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010   $a3-319-33596-0
024 7 $a10.1007/978-3-319-33596-4
035   $a(CKB)3710000000734711
035   $a(EBL)4573595
035   $a(DE-He213)978-3-319-33596-4
035   $a(MiAaPQ)EBC4573595
035   $a(PPN)194381390
035   $a(EXLCZ)993710000000734711
100   $a20160610d2016      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 14$aThe Parabolic Anderson Model $eRandom Walk in Random Potential /$fby Wolfgang König
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2016.
215   $a1 online resource (199 p.)
225 1 $aPathways in Mathematics,$x2367-3451
300   $aDescription based upon print version of record.
311   $a3-319-33595-2 
320   $aIncludes bibliographical references and index.
327   $a1 Background, model and questions -- 2 Tools and concepts -- 3 Moment asymptotics for the total mass -- 4 Some proof techniques -- 5 Almost sure asymptotics for the total mass -- 6 Strong intermittency -- 7 Refined questions -- 8 Time-dependent potentials.
330   $aThis is a comprehensive survey on the research on the parabolic Anderson model ? the heat equation with random potential or the random walk in random potential ? of the years 1990 ? 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.
410  0$aPathways in Mathematics,$x2367-3451
606   $aProbabilities
606   $aMathematical physics
606   $aPhysics
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120
606   $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013
615  0$aProbabilities.
615  0$aMathematical physics.
615  0$aPhysics.
615 14$aProbability Theory and Stochastic Processes.
615 24$aMathematical Applications in the Physical Sciences.
615 24$aMathematical Methods in Physics.
676   $a510
700   $aKönig$b Wolfgang$4aut$4http://id.loc.gov/vocabulary/relators/aut$094143
906   $aBOOK
912   $a9910254098203321
996   $aThe Parabolic Anderson Model$92235917
997   $aUNINA