Itô diffusions, modified capacity and harmonic measure. Applications to Schrödinger operators.
| hal.structure.identifier | Department of Mathematics [Madison] | |
| dc.contributor.author | DENISSOV, Sergey | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | KUPIN, Stanislas | |
| dc.date.accessioned | 2024-04-04T02:22:45Z | |
| dc.date.available | 2024-04-04T02:22:45Z | |
| dc.date.created | 2011 | |
| dc.date.issued | 2012 | |
| dc.identifier.issn | 1073-7928 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189672 | |
| dc.description.abstractEn | We observe that some special Itô diffusions are related to scattering properties of a Schrödinger operator on R^d, d>1. We introduce Feynman-Kac type formulae for these stochastic processes which lead us to results on the preservation of the a.c. spectrum of the Schrödinger operator. To better understand the analytic properties of the processes, we construct and study a special version of the potential theory. The modified capacity and harmonic measure play an important role in these considerations. Various applications to Schrödinger operators are also given. For example, we relate the presence of the absolutely continuous spectrum to the geometric properties of the support of the potential. | |
| dc.language.iso | en | |
| dc.publisher | Oxford University Press (OUP) | |
| dc.subject.en | Absolutely continuous spectrum | |
| dc.subject.en | Schrödinger operator | |
| dc.subject.en | Itô stochastic calculus | |
| dc.subject.en | Feynman-Kac type formulae | |
| dc.subject.en | special potential theory | |
| dc.subject.en | modified capacity | |
| dc.subject.en | modified harmonic measure | |
| dc.title.en | Itô diffusions, modified capacity and harmonic measure. Applications to Schrödinger operators. | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| bordeaux.journal | International Mathematics Research Notices | |
| bordeaux.page | 3127-3181 | |
| bordeaux.volume | 14 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00781333 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00781333v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=International%20Mathematics%20Research%20Notices&rft.date=2012&rft.volume=14&rft.spage=3127-3181&rft.epage=3127-3181&rft.eissn=1073-7928&rft.issn=1073-7928&rft.au=DENISSOV,%20Sergey&KUPIN,%20Stanislas&rft.genre=article |
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