Ecole d'Eté de Probabilités de Saint-Flour XIV, 1984:
Gespeichert in:
| Körperschaft: | |
|---|---|
| Format: | Tagungsbericht Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1986
|
| Schriftenreihe: | Lecture notes in mathematics
1180 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 439 S. |
| ISBN: | 3540164413 0387164413 |
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Datensatz im Suchindex
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| adam_text | TABLE.DES,MATIERES
it=£âSËQMa : RANDOM SCHRODINGER OPERATORS
PREFACE ¦ 2
0. INTRODUCTION 3
1. SPECTRAL THEORY OF SELF ADJOINT OPERATORS 8
1.1. Domains, adjoints, resolvents and spectra 8
1.2. Resolutions of the identity 12
1.3. Représentation theorems 17
1.4. The spectral theorem 19
1.5. Perturbations and quadratic foras 22
1.6. Self adjoint extensions of symmetric operators 23
1.7. Références 24
II. MEASURABILITY AND ERGODICITY OF SELF ADJOINT OPERATORS 25
II. 1. Measurability 25
11.2. Spectra in the ergodic case 30
11.3. Comments 40
III. SCHRODINGER OPERATORS 41
111.1. The free Lapiacians 41
111.2. The perturbed Laplacians 44
111.3. The one dimensional case 46
.11,4. Compléments : the Feynman Kac and Molcanov formulae 53
IV. RANDOM SCHRODINGER OPERATORS 57
IV.. 1. Essential self adjointness and measurability 57
IV.2. Examples 60
¦ IV.3. Compléments 63
V. THE INTEGRATED DENSITY OF STATES 64
V.1. Existence in the continuous case 65
V.2. Asymptotic behavior 72
V.3. The lattice case 75
V.4. The one dimensional case 80
V.5. Compléments and comments 89
VIII
VI. THE ABSOLUTELY CONTINUOUS SPECTRUM IN ONE DIMENSION 92
VI.1. The Ljapunov exponent 92
VI.2, The Ishii Pastur resuit 96
VI.3. Kotani s converse 97
VI.4. Compléments and bibliographical commenta 100
VII. EXPONENTIAL LOCALIZATION IN ONE DIMENSION 102
VII.1. Informai discussion 103
VII.2. A proof . 105
VII.3. Compléments 111
REFERENCES 114
Notations 122
Index 123
Bi=SliI|| : ASPECTS OF FIRST PASSAGE PERCOLATION
1. Introduction 126
2. Kïngman s subadditive ercjodic theorem and the tirae constant 134
3. The asyroptotic shape of B(t) and B(t) 154
4. Some inequalities 168
5. The rate of convergence to the tirae constant 180
6. Propertles of the tirae constant y and the litnit set BQ 218
7. The rate of convergence to the time constant revisited : the
case p = 0 (and d = 2) 231
8. Asyraptotics for large dimensions 239
9. Maximal flows and other open problems 249
Références 260
INDEX 263
IX
JJkJtfALSH : AN INTRODUCTION TQ STOCHASTIC PARTIAL BIFFERENTIAL EQUATIONS
INTRODUCTION 266
CHAPTER I 269
White noise and the Brownian sheet 269
Sample function properties 271
Some remarks on the Markov property , 276
The propagation of singularities 279
The Brownian sheet and the vibrating string 281
White noise as a distribution 284
CHAPTER II 286
Martingale roeasures 286
Worthy measures 289
Stochastic intégrais 292
Orthogonal measures 298
Nuclear covariance 303
An example 305
CHAPTER III 308
Equations in one space dimension 308
The wave équation 308
An example arising in neurophysiology 311
The linear équation 323
The Barrïer problem 326
Higher dimensions 328
CHAPTER IV 330
Distribution val ued processes 330
Regularization 332
Examples 334
CHAPTER V 339
Parabolic équations in R 339
An eigenfunction expansion 343
CHAPTER VI 349
Weak convergence 349
Aldous1 theorera 354
Mitoma s theorem 358
X
CHAPTER VII 365
Applications of weak convergence 365
Weak convergence of stochastic intégrais 367
An application 373
An extension 376
CHAPTER VIII 385
The Brownian density process 385
The fundamental noises 388
Weak convergence in the Gaussian case 393
A measure diffusion 398
The case y/À *• °° 400
The square of the Brownian density process 407
CHAPTER IX 415
Limîts of the Brownian density process 417
Connection with spde s 419
Smoothness 420
The Markov property fo the free field 420
NOTES 423
REFERENCES 432
INDEX 437.
|
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| illustrated | Not Illustrated |
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| language | English |
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| spelling | Ecole d'Eté de Probabilités 14 1984 Saint-Flour Verfasser (DE-588)667366-1 aut Ecole d'Eté de Probabilités de Saint-Flour XIV, 1984 R. Carmona ; H. Kesten ; J. B. Walsh. Ed. par P. L. Hennequin Berlin [u.a.] Springer 1986 X, 439 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1180 Percolation (Statistical physics) Probabilities Schrödinger operator Stochastic partial differential equations Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1984 Saint-Flour gnd-content Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Carmona, René 1947- Sonstige (DE-588)122405668 oth Kesten, Harry 1931-2019 Sonstige (DE-588)121449300 oth Walsh, John B. Sonstige (DE-588)139897658 oth Hennequin, Paul L. Sonstige (DE-588)1067948570 oth Lecture notes in mathematics 1180 (DE-604)BV000676446 1180 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000295956&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ecole d'Eté de Probabilités de Saint-Flour XIV, 1984 Lecture notes in mathematics Percolation (Statistical physics) Probabilities Schrödinger operator Stochastic partial differential equations Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)1071861417 |
| title | Ecole d'Eté de Probabilités de Saint-Flour XIV, 1984 |
| title_auth | Ecole d'Eté de Probabilités de Saint-Flour XIV, 1984 |
| title_exact_search | Ecole d'Eté de Probabilités de Saint-Flour XIV, 1984 |
| title_full | Ecole d'Eté de Probabilités de Saint-Flour XIV, 1984 R. Carmona ; H. Kesten ; J. B. Walsh. Ed. par P. L. Hennequin |
| title_fullStr | Ecole d'Eté de Probabilités de Saint-Flour XIV, 1984 R. Carmona ; H. Kesten ; J. B. Walsh. Ed. par P. L. Hennequin |
| title_full_unstemmed | Ecole d'Eté de Probabilités de Saint-Flour XIV, 1984 R. Carmona ; H. Kesten ; J. B. Walsh. Ed. par P. L. Hennequin |
| title_short | Ecole d'Eté de Probabilités de Saint-Flour XIV, 1984 |
| title_sort | ecole d ete de probabilites de saint flour xiv 1984 |
| topic | Percolation (Statistical physics) Probabilities Schrödinger operator Stochastic partial differential equations Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Percolation (Statistical physics) Probabilities Schrödinger operator Stochastic partial differential equations Wahrscheinlichkeitsrechnung Konferenzschrift 1984 Saint-Flour |
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