01111nam a22002651i 450099100223450970753620040219130920.0040407s2001 ne |||||||||||||||||eng 9004121552b12891563-39ule_instARCHE-087118ExLDip.to Filologia Class. e Scienze FilosoficheitaA.t.i. Arché s.c.r.l. Pandora Sicilia s.r.l.306.8108Phang, Sara Elise486278The marriage of Roman soldiers (13 b. C.-A. D. 235) :law and family in the imperial army /by Sara Elise PhangLeiden [etc.] :Brill,2001VI, 470 p. ;24 cmColumbia studies in the classical tradition ;24Matrimonio dei militariDiritto romano.b1289156302-04-1416-04-04991002234509707536LE007 340 PHA 01.0112007000068335le007-E0.00-l- 00000.i1345555216-04-04Marriage of Roman soldiers (13 b. C.-A. D. 235)305498UNISALENTOle00716-04-04ma -engne 4103364nam 22005655 450 991025409820332120200702201007.03-319-33596-010.1007/978-3-319-33596-4(CKB)3710000000734711(EBL)4573595(DE-He213)978-3-319-33596-4(MiAaPQ)EBC4573595(PPN)194381390(EXLCZ)99371000000073471120160610d2016 u| 0engur|n|---|||||txtrdacontentcrdamediacrrdacarrierThe Parabolic Anderson Model Random Walk in Random Potential /by Wolfgang König1st ed. 2016.Cham :Springer International Publishing :Imprint: Birkhäuser,2016.1 online resource (199 p.)Pathways in Mathematics,2367-3451Description based upon print version of record.3-319-33595-2 Includes bibliographical references and index.1 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.This 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.Pathways in Mathematics,2367-3451ProbabilitiesMathematical physicsPhysicsProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Mathematical Applications in the Physical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13120Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Probabilities.Mathematical physics.Physics.Probability Theory and Stochastic Processes.Mathematical Applications in the Physical Sciences.Mathematical Methods in Physics.510König Wolfgangauthttp://id.loc.gov/vocabulary/relators/aut94143BOOK9910254098203321The Parabolic Anderson Model2235917UNINA