000 03162nam a22004935i 4500
001 978-3-540-46627-7
003 DE-He213
005 20190213151242.0
007 cr nn 008mamaa
008 130109s1991 gw | s |||| 0|eng d
020 _a9783540466277
_9978-3-540-46627-7
024 7 _a10.1007/BFb0093929
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aLang, Reinhard.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSpectral Theory of Random Schrödinger Operators
_h[electronic resource] :
_bA Genetic Introduction /
_cby Reinhard Lang.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1991.
300 _aX, 126 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1498
505 0 _aTwo simple examples -- The general heuristic picture -- Some known results and open problems -- Explanation of Theorem 1 and introduction to an extended Boltzmann theory of entropy -- Explanation of Theorem 2 and introduction to an extended Floquet-Weyl theory -- Conclusion.
520 _aThe interplay between the spectral theory of Schr|dinger operators and probabilistic considerations forms the main theme of these notes, written for the non-specialist reader and intended to provide a brief and elementaryintroduction to this field. An attempt is made to show basic ideas in statu nascendi and to follow their evaluation from simple beginnings through to more advanced results. The term "genetic" in the title refers to this proceedure. The author concentrates on 2 topics which, in the history of the subject, have been of major conceptual importance - on the one hand the Laplacian is a random medium and the left end of its spectrum (leading to large deviation problems for Brownian motion and the link to thenotion of entropy) and on the other, Schr|dinger operators with general ergodic potentials in one-dimensional space. Ideas and concepts are explained in the simplest, possible setting and by means of a few characteristic problems with heuristic arguments preceding rigorous proofs.
650 0 _aDistribution (Probability theory.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662191514
776 0 8 _iPrinted edition:
_z9783540549758
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1498
856 4 0 _uhttps://doi.org/10.1007/BFb0093929
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10038
_d10038