Random Witten Laplacians: traces of semigroups, L 2-Betti numbers and index
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Bonn
SFB 611
2006
|
| Series: | Sonderforschungsbereich 611, Singuläre Phänomene und Skalierung in Mathematischen Modellen
295 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 40 S. |
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Record in the Search Index
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| adam_text | RANDOM WITTEN LAPLACIANS: TRACES OF SEMIGROUPS, L^BETTI NUMBERS AND
INDEX SERGIO ALBEVERIO, ALEXEI DALETSKII, ALEXANDER KALYUZHNYI NO. 295
SUB GOTTINGEN 7 220 385 017 K2007B5068 DIESE ARBEIT IST MIT
UNTERSTUTZUNG DES VON DER DEUTSCHEN FORSCHUNGS- GEMEINSCHAFT GETRAGENEN
SONDERFORSCHUNGSBEREICHES 611 AN DER UNIVER- SITAT BONN ENTSTANDEN UND
ALS MANUSKRIPT VERVIELFALTIGT WORDEN. BONN, OKTOBER 2006 CONTENTS 1
INTRODUCTION 1 2 RANDOM WITTEN LAPLACIAN 6 3 PROBABILISTIC
REPRESENTATION OF THE HEAT KERNELS 9 4 VON NEUMANN ALGEBRAS ASSOCIATED
WITH RANDOM LAPLACIANS 15 5 STABILITY OF THE INDEX 20 6 EXAMPLES 25 6.1
GASES 25 6.1.1 CONFIGURATION SPACES AND MEASURES 25 6.1.2 PROBABILISTIC
REPRESENTATIONS OF LAPLACIANS .26 6.2 CRYSTALS 29 6.2.1 PRODUCT
MEASURES. 30 6.2.2 GIBBS MEASURES 31 7 APPENDIX: GIBBS MEASURES 33 7.1
GIBBS MEASURES ON CONFIGURATION SPACES. ., 33 7.2 GIBBS MEASURES ON
PRODUCT MANIFOLDS 35 1 INTRODUCTION RANDOM OPERATORS, IN PARTICULAR,
SCHRODINGER OPERATORS WITH RANDOM POTEN- TIALS, PLAY AN IMPORTANT ROLE
IN DIFFERENT PARTS OF MATHEMATICS AND. MATHE- MATICAL PHYSICS, SEE E.G.
[32]. A CRUCIAL ROLE IN THIS THEORY IS PLAYED BY THE CONCEPT OF METRIC
TRANSITIVITY. A RANDOM OPERATOR I/ 7 , 76$, WHERE ^ IS A PROBABILITY
SPACE, ACTING IN A HILBERT SPACE 7I, IS SAID TO BE METRICALLY TRAN-
SITIVE, IF THERE EXISTS A GROUP G OF MEASURE-PRESERVING TRANSFORMATIONS
OF ^ AND A UNITARY REPRESENTATION U G OF G IN H SUCH THAT 1) ITS ACTION
ON ^ IS ERGODIC, AND 2) FR ANY G E G AND 76$ THE FOLLOWING COMMUTATION
RELATION HOLDS: U 9 -IH^U G = H GI . (1)
|
| adam_txt |
RANDOM WITTEN LAPLACIANS: TRACES OF SEMIGROUPS, L^BETTI NUMBERS AND
INDEX SERGIO ALBEVERIO, ALEXEI DALETSKII, ALEXANDER KALYUZHNYI NO. 295
SUB GOTTINGEN 7 220 385 017 K2007B5068 DIESE ARBEIT IST MIT
UNTERSTUTZUNG DES VON DER DEUTSCHEN FORSCHUNGS- GEMEINSCHAFT GETRAGENEN
SONDERFORSCHUNGSBEREICHES 611 AN DER UNIVER- SITAT BONN ENTSTANDEN UND
ALS MANUSKRIPT VERVIELFALTIGT WORDEN. BONN, OKTOBER 2006 CONTENTS 1
INTRODUCTION 1 2 RANDOM WITTEN LAPLACIAN 6 3 PROBABILISTIC
REPRESENTATION OF THE HEAT KERNELS 9 4 VON NEUMANN ALGEBRAS ASSOCIATED
WITH RANDOM LAPLACIANS 15 5 STABILITY OF THE INDEX 20 6 EXAMPLES 25 6.1
GASES 25 6.1.1 CONFIGURATION SPACES AND MEASURES 25 6.1.2 PROBABILISTIC
REPRESENTATIONS OF LAPLACIANS .26 6.2 CRYSTALS 29 6.2.1 PRODUCT
MEASURES. 30 6.2.2 GIBBS MEASURES 31 7 APPENDIX: GIBBS MEASURES 33 7.1
GIBBS MEASURES ON CONFIGURATION SPACES. ., 33 7.2 GIBBS MEASURES ON
PRODUCT MANIFOLDS 35 1 INTRODUCTION RANDOM OPERATORS, IN PARTICULAR,
SCHRODINGER OPERATORS WITH RANDOM POTEN- TIALS, PLAY AN IMPORTANT ROLE
IN DIFFERENT PARTS OF MATHEMATICS AND. MATHE- MATICAL PHYSICS, SEE E.G.
[32]. A CRUCIAL ROLE IN THIS THEORY IS PLAYED BY THE CONCEPT OF METRIC
TRANSITIVITY. A RANDOM OPERATOR I/ 7 , 76$, WHERE ^ IS A PROBABILITY
SPACE, ACTING IN A HILBERT SPACE 7I, IS SAID TO BE METRICALLY TRAN-
SITIVE, IF THERE EXISTS A GROUP G OF MEASURE-PRESERVING TRANSFORMATIONS
OF ^ AND A UNITARY REPRESENTATION U G OF G IN H SUCH THAT 1) ITS ACTION
ON ^ IS ERGODIC, AND 2) FR ANY G E G AND 76$ THE FOLLOWING COMMUTATION
RELATION HOLDS: U 9 -IH^U G = H GI . (1) |
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| author | Albeverio, Sergio 1939- Daletskij, Aleksej Kaljužnyj, Aleksandr |
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| series | Sonderforschungsbereich 611, Singuläre Phänomene und Skalierung in Mathematischen Modellen |
| series2 | Sonderforschungsbereich 611, Singuläre Phänomene und Skalierung in Mathematischen Modellen |
| spelling | Albeverio, Sergio 1939- Verfasser (DE-588)121093999 aut Random Witten Laplacians traces of semigroups, L 2-Betti numbers and index Sergio Albeverio, Alexei Daletskii, Alexander Kalyuzhnyi Bonn SFB 611 2006 40 S. txt rdacontent n rdamedia nc rdacarrier Sonderforschungsbereich 611, Singuläre Phänomene und Skalierung in Mathematischen Modellen 295 Daletskij, Aleksej Verfasser aut Kaljužnyj, Aleksandr Verfasser aut Sonderforschungsbereich 611, Singuläre Phänomene und Skalierung in Mathematischen Modellen 295 (DE-604)BV014653850 295 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015513448&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Albeverio, Sergio 1939- Daletskij, Aleksej Kaljužnyj, Aleksandr Random Witten Laplacians traces of semigroups, L 2-Betti numbers and index Sonderforschungsbereich 611, Singuläre Phänomene und Skalierung in Mathematischen Modellen |
| title | Random Witten Laplacians traces of semigroups, L 2-Betti numbers and index |
| title_auth | Random Witten Laplacians traces of semigroups, L 2-Betti numbers and index |
| title_exact_search | Random Witten Laplacians traces of semigroups, L 2-Betti numbers and index |
| title_exact_search_txtP | Random Witten Laplacians traces of semigroups, L 2-Betti numbers and index |
| title_full | Random Witten Laplacians traces of semigroups, L 2-Betti numbers and index Sergio Albeverio, Alexei Daletskii, Alexander Kalyuzhnyi |
| title_fullStr | Random Witten Laplacians traces of semigroups, L 2-Betti numbers and index Sergio Albeverio, Alexei Daletskii, Alexander Kalyuzhnyi |
| title_full_unstemmed | Random Witten Laplacians traces of semigroups, L 2-Betti numbers and index Sergio Albeverio, Alexei Daletskii, Alexander Kalyuzhnyi |
| title_short | Random Witten Laplacians |
| title_sort | random witten laplacians traces of semigroups l 2 betti numbers and index |
| title_sub | traces of semigroups, L 2-Betti numbers and index |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015513448&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014653850 |
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