Lectures on probability theory and statistics:
Saved in:
| Format: | Conference Proceeding Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Series: | Lecture notes in mathematics
1665 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 424 S. |
| ISBN: | 3540631909 |
Staff View
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| 245 | 1 | 0 | |a Lectures on probability theory and statistics |c Ecole d'Eté de Probabilités de Saint-Flour XXVI - 1996. E. Giné ... Ed.: P. Bernard |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
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Record in the Search Index
| _version_ | 1804125950235901952 |
|---|---|
| adam_text | TABLE
OF
CONTENTS
Evarist
GINE
:
DECOUPLING AND LIMIT THEOREMS
FOR U-STATISTICS AND U-PROCESSES
1
1.
Introduction
2
2.
Decoupling inequalities
3
3.
Limit theorems for U-statistics
12
4.
Limit theorems for U-processes
24
References
32
Evarist
GINE
:
LECTURES ON SOME ASPECTS
THEORY OF THE BOOTSTRAP
37
Preface
39
1.
On the bootstrap in
R
41
1.1
Efron s bootstrap of the mean in
R
41
1.2
The general exchangeable bootstrap of the mean
54
1.3
The bootstrap of the mean for stationary sequences
59
1.4
The bootstrap of U-statistics
64
1.5
A general
m
out of
n
bootstrap
76
2.
On the bootstrap for empirical processes
83
2.1
Background from empirical process theory
83
2.2
Poissonization inequalities and Efron s bootstrap in probability
103
2.3
The almost sure Efron s bootstrap
113
2.4
The exchangeable bootstrap
119
2.5
Uniformly pregaussian classes of functions and the bootstrap
128
2.6
Some remarks on applications
139
References
147
VIII
Geoffrey GRIMMETT
:
«PERCOLATION AND
DISORDERED SYSTEMS
153
Preface 154
1.
Introductory Remarks 158
1.1
Percolation Ijjjj
1.2
Some possible questions Lt3°
1.3
History 159
2.
Notation and Definitions
161
2.1
Graph terminology
161
2.2
Probability 162
2.3
Geometry 162
2.4
A partial order 164
2.5
Site percolation 165
3.
Phase Transition
166
3.1
Percolation probability
166
3.2
Existence of phase transition
166
3.3
A question
168
4.
Inequalities for Critical Probabilities
169
4.1
Russo s formula
169
4.2
Strict inequalities for critical probabilities
171
4.3
The square and triangular lattices
172
4.4
Enhancements
176
5.
Correlation Inequalities
178
5.1
FKG inequality
178
5.2
Disjoint occurrence
181
5.3
Site and bond percolation
182
6.
Subcriticai
Percolation
185
6.1
Using subadditivity
185
6.2
Exponential decay
188
6.3
Ornstein-Zernike decay
198
IX
7.
Supercritical
Percolation
199
7.1
Uniqueness of the infinite
cluster
199
7.2
Percolation in slabs
201
7.3
Limit of slab critical points
202
7.4
Percolation in half-spaces
215
7.5
Percolation probability
216
7.6
Cluster-size distribution
218
8.
Critical Percolation
219
8.1
Percolation probability
219
8.2
Critical exponents
219
8.3
Scaling theory
219
8.4
Rigorous results
221
8.5
Mean-field theory
221
9.
Percolation in Two Dimensions
229
9.1
The critical probability is
1/2 229
9.2
RS W
technology
230
9.3
Conformai invariance
233
10.
Random Walks in Random Labyrinths
236
10.1
Random walk on the infinite percolation cluster
236
10.2
Random walks in two-dimensional labyrinths
240
10.3
General labyrinths
248
11.
Fractal Percolation
254
11.1
Random fractals
254
11.2
Percolation
255
11.3
A morphology
258
11.4
Relationship to Brownian Motion
260
12.
Ising and Potts Models
261
12.1
bing
model for ferromagnets
261
12.2
Potts models
262
12.3
Random-cluster models
263
13.
Random-Cluster Models
265
13.1
Basic properties
265
13.2
Weak limits and phase transitions
266
13.3
First and second order transitions
268
13.4
Exponential decay in the
subcriticai
phase
269
13.5
The case of two dimensions
273
References
281
Laurent SALOFF-COSTE :
LECTURES ON
FINITE
MARKOV CHAINS
301
1.
Introduction and background material
304
1.1
Introduction
304
1.2
The Perron-Frobenius Theorem
309
1.3
Notation for finite Markov chains
319
2.
Analytic tools
326
2.1
Nothing but the spectral gap
326
2.2
Hypercontractivity
332
2.3
Nash inequalities
344
2.4
Distances
358
3.
Geometric tools
367
3.1
Adapted edge sets
368
3.2
Poincaré
inequality
368
3.3
Isopemnetry
379
3.4
Moderate growth
394
4.
Comparison techniques
396
4.1
Using comparison inequalities
396
4.2
Comparison of Dirichlet forms using paths
400
Bibliography
408
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Conference Proceeding Book |
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| spelling | Lectures on probability theory and statistics Ecole d'Eté de Probabilités de Saint-Flour XXVI - 1996. E. Giné ... Ed.: P. Bernard Berlin [u.a.] Springer 1997 X, 424 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1665 Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1996 Saint-Flour gnd-content Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Statistik (DE-588)4056995-0 s 1\p DE-604 DE-604 Giné, Evarist 1944-2015 Sonstige (DE-588)128482494 oth Grimmett, Geoffrey 1950- Sonstige (DE-588)120872919 oth Saloff-Coste, Laurent 1958- Sonstige (DE-588)115395776 oth Bernard, Pierre Sonstige oth Ecole d'Eté de Probabilités 26 1996 Saint-Flour Sonstige (DE-588)2163895-0 oth Lecture notes in mathematics 1665 (DE-604)BV000676446 1665 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007689735&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lectures on probability theory and statistics Lecture notes in mathematics Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4079013-7 (DE-588)1071861417 |
| title | Lectures on probability theory and statistics |
| title_auth | Lectures on probability theory and statistics |
| title_exact_search | Lectures on probability theory and statistics |
| title_full | Lectures on probability theory and statistics Ecole d'Eté de Probabilités de Saint-Flour XXVI - 1996. E. Giné ... Ed.: P. Bernard |
| title_fullStr | Lectures on probability theory and statistics Ecole d'Eté de Probabilités de Saint-Flour XXVI - 1996. E. Giné ... Ed.: P. Bernard |
| title_full_unstemmed | Lectures on probability theory and statistics Ecole d'Eté de Probabilités de Saint-Flour XXVI - 1996. E. Giné ... Ed.: P. Bernard |
| title_short | Lectures on probability theory and statistics |
| title_sort | lectures on probability theory and statistics |
| topic | Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Statistik Wahrscheinlichkeitstheorie Konferenzschrift 1996 Saint-Flour |
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