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The Resource Probability theory and applications, Elton P. Hsu, S.R.S. Varadhan, editors

Probability theory and applications, Elton P. Hsu, S.R.S. Varadhan, editors

Label
Probability theory and applications
Title
Probability theory and applications
Statement of responsibility
Elton P. Hsu, S.R.S. Varadhan, editors
Contributor
Subject
Genre
Language
eng
Member of
Cataloging source
DLC
Dewey number
519.2
Illustrations
illustrations
Index
no index present
LC call number
QA273.A1
LC item number
P768 1999
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
  • 1959-
  • 1996
http://library.link/vocab/relatedWorkOrContributorName
  • Hsu, Elton P.
  • Varadhan, S. R. S
  • Graduate Summer School Program on Probability Theory
Series statement
IAS/Park City mathematics series,
Series volume
v. 6
http://library.link/vocab/subjectName
  • Probabilities
  • Waarschijnlijkheidstheorie
  • Kongress
  • Wahrscheinlichkeitstheorie
Label
Probability theory and applications, Elton P. Hsu, S.R.S. Varadhan, editors
Instantiates
Publication
Note
"Lecture notes from the Graduate Summer School Program on Probability Theory, held in Princeton, NJ, on June 23-July 13, 1996"--T.p. verso
Bibliography note
Includes bibliographical references (pages 373-374)
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Basic dichotomy
  • 137
  • The BC decoupling inequalities
  • 139
  • Comparison principles
  • 143
  • The DLR equation and states of the random cluster model
  • 146
  • Length scales in the Potts models
  • 152
  • Hydrodynamical Scaling Limits of Simple Exclusion Models
  • 10
  • Leif Jensen, Horng-Tzer Yau
  • 167
  • Lecture 1.
  • The Simple Exclusion Model
  • 171
  • The configuration space
  • 171
  • The dynamics
  • 171
  • The generator
  • Lecture 2.
  • 172
  • Reversibility
  • 173
  • Ito's formula and current
  • 174
  • Time-space scaling
  • 175
  • Macroscopic profiles
  • 176
  • Contents of the following lectures
  • Coalescing Random Walks
  • 178
  • Lecture 2.
  • Proof of Theorem 1.4
  • 181
  • Tightness
  • 181
  • Properties of the weak hydrodynamical equation
  • 182
  • Identification of the hydrodynamical equation
  • 183
  • 13
  • Lecture 3.
  • Local Ergodicity
  • 187
  • Lecture 4.
  • Two-Block Estimate
  • 193
  • Lecture 5.
  • Relative Entropy
  • 197
  • Asymmetric simple exclusion
  • Lecture 3.
  • 199
  • Lecture 6.
  • The Green-Kubo Formula and Asymmetric Simple Exclusion Processes
  • 205
  • Lecture 7.
  • Some Open Problems
  • 217
  • An Introduction to Analysis on Path Space
  • Daniel W. Stroock
  • 227
  • Voter Model with Mutation
  • Lecture 1.
  • Gaussian Measures on a Hilbert Space
  • 231
  • The finite dimensional case
  • 231
  • The infinite dimensional case
  • 232
  • Construction of Wiener measure
  • 233
  • A few variations
  • 19
  • 236
  • Lecture 2.
  • Rolling On
  • 241
  • The idea
  • 241
  • The rolling map
  • 241
  • The orthonormal frame bundle
  • 243
  • Species-area curves
  • Extending the rolling map
  • 245
  • Lecture 3.
  • About Wm
  • 253
  • Martingale properties
  • 253
  • Fun and games with Bochner's identity
  • 256
  • Lecture 4.
  • 20
  • A Few Facts, and Something Else
  • 261
  • H[superscript 1] ([0, [infinity]); M) as a Riemannian manifold
  • 261
  • An affine connection and its geodesics
  • 263
  • Perturbing paths along geodesics and Driver's formula
  • 265
  • Some comments and extensions
  • 270
  • Stochastic Spatial Models
  • Species abundance distributions
  • Analysis on Path and Loop Spaces
  • Elton P. Hsu
  • 277
  • Lecture 1.
  • Euclidean Brownian Motion
  • 281
  • Definition of euclidean Brownian motion
  • 281
  • Basic properties
  • 283
  • 22
  • Quasi-invariance of the Wiener measure
  • 284
  • Brownian bridge
  • 285
  • Quasi-invariance of the Wiener measure in loop space
  • 287
  • Lecture 2.
  • Gradient Operator
  • 291
  • Gradient operator
  • Local limit theorems
  • 291
  • Integration by parts
  • 293
  • Closability of the gradient operator
  • 295
  • Gradient operator in flat loop space
  • 296
  • Lecture 3.
  • Ornstein-Uhlenbeck Operator
  • 299
  • 23
  • Definition and basic properties
  • 299
  • Spectrum of the Ornstein-Uhlenbeck operator
  • 301
  • Logarithmic Sobolev inequality
  • 304
  • Hypercontractivity of the Ornstein-Uhlenbeck semigroup
  • 305
  • Lecture 4.
  • Brownian Motion on Manifolds
  • Lecture 4.
  • 309
  • Preliminaries
  • 309
  • Construction of Riemannian Brownian motion
  • 311
  • Horizontal lift of Brownian motion
  • 313
  • Lecture 5.
  • Gradient Formulas
  • 319
  • The Block Construction
  • A commutation relation
  • 319
  • Gradient formula I
  • 321
  • Gradient formula II
  • 323
  • Bismut's formula for the gradient of the heat kernel
  • 324
  • Lecture 6.
  • Integration by Parts
  • 27
  • 325
  • Gradient operator in the path space
  • 325
  • Integration by parts in path space
  • 327
  • Brownian bridge on Riemannian manifolds
  • 329
  • Integration by parts in the loop space
  • 331
  • Lecture 7.
  • Oriented percolation
  • Logarithmic Sobolev Inequalities
  • 337
  • Martingale representation theorem
  • 337
  • Proof of the main result
  • 339
  • Generalized Ornstein-Uhlenbeck operator
  • 341
  • An Introduction to Option Pricing and the Mathematical Theory of Risk
  • Marco Avellaneda
  • 27
  • 349
  • Investments and probability
  • 352
  • Options
  • 354
  • Risk-neutral probabilities
  • 358
  • Risk-management using the "Greeks"
  • 361
  • Uncertain volatility models
  • The stability theorem of Gray and Griffeath
  • 365
  • Relative entropy: combining volatility uncertainty with a-priori beliefs
  • 369
  • Rick Durrett
  • 30
  • Lecture 5.
  • Long Range Limits
  • 35
  • Estimation for the limit system
  • 37
  • Continuity argument
  • 37
  • Lecture 6.
  • Rapid Stirring Limits
  • 5
  • 39
  • Independent and Dependent Percolation
  • Jennifer Tour Chayes, Amber L. Puha, Ted Sweet
  • 49
  • Lecture 1.
  • The Basics of Percolation
  • 53
  • Relevant quantities and expected behavior
  • 53
  • Basic techniques
  • Lecture 1.
  • 62
  • Lecture 2.
  • Rescaling and Finite-Size Scaling in Percolation
  • 67
  • Rescaling and characterization of phases (d = 2)
  • 67
  • Finite-size scaling and the correlation length
  • 72
  • Lecture 3.
  • Critical Exponent Inequalities
  • The Voter Model
  • 81
  • A bound on the correlation length via finite-size scaling events
  • 81
  • Mean-field bounds
  • 86
  • Lecture 4.
  • Two Fundamental Questions
  • 93
  • Absence of an intermediate phase
  • 93
  • 9
  • Uniqueness of the infinite cluster
  • 99
  • Lecture 5.
  • Finite-Size Scaling and the Incipient Infinite Cluster
  • 105
  • The motivation
  • 105
  • Definitions of relevant quantities and preliminaries
  • 108
  • The scaling axioms and the results
  • Construction and duality
  • 111
  • Interpretation of the results
  • 117
  • Lecture 6.
  • The BK(R) Inequality
  • 119
  • Equivalent forms of the inequality
  • 119
  • Preliminaries to the proof of the BK inequality
  • 121
  • 9
  • The proof of the BK inequality
  • 122
  • Lecture 7.
  • The Potts Model and the Random Cluster Model
  • 129
  • The Potts models
  • 130
  • The Fortuin-Kasteleyn representation
  • 134
  • Standard correlation inequalities
Control code
40359464
Dimensions
27 cm
Extent
x, 374 pages
Isbn
9780821805909
Isbn Type
(hc. : alk. paper)
Lccn
98051767
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)40359464
Label
Probability theory and applications, Elton P. Hsu, S.R.S. Varadhan, editors
Publication
Note
"Lecture notes from the Graduate Summer School Program on Probability Theory, held in Princeton, NJ, on June 23-July 13, 1996"--T.p. verso
Bibliography note
Includes bibliographical references (pages 373-374)
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Basic dichotomy
  • 137
  • The BC decoupling inequalities
  • 139
  • Comparison principles
  • 143
  • The DLR equation and states of the random cluster model
  • 146
  • Length scales in the Potts models
  • 152
  • Hydrodynamical Scaling Limits of Simple Exclusion Models
  • 10
  • Leif Jensen, Horng-Tzer Yau
  • 167
  • Lecture 1.
  • The Simple Exclusion Model
  • 171
  • The configuration space
  • 171
  • The dynamics
  • 171
  • The generator
  • Lecture 2.
  • 172
  • Reversibility
  • 173
  • Ito's formula and current
  • 174
  • Time-space scaling
  • 175
  • Macroscopic profiles
  • 176
  • Contents of the following lectures
  • Coalescing Random Walks
  • 178
  • Lecture 2.
  • Proof of Theorem 1.4
  • 181
  • Tightness
  • 181
  • Properties of the weak hydrodynamical equation
  • 182
  • Identification of the hydrodynamical equation
  • 183
  • 13
  • Lecture 3.
  • Local Ergodicity
  • 187
  • Lecture 4.
  • Two-Block Estimate
  • 193
  • Lecture 5.
  • Relative Entropy
  • 197
  • Asymmetric simple exclusion
  • Lecture 3.
  • 199
  • Lecture 6.
  • The Green-Kubo Formula and Asymmetric Simple Exclusion Processes
  • 205
  • Lecture 7.
  • Some Open Problems
  • 217
  • An Introduction to Analysis on Path Space
  • Daniel W. Stroock
  • 227
  • Voter Model with Mutation
  • Lecture 1.
  • Gaussian Measures on a Hilbert Space
  • 231
  • The finite dimensional case
  • 231
  • The infinite dimensional case
  • 232
  • Construction of Wiener measure
  • 233
  • A few variations
  • 19
  • 236
  • Lecture 2.
  • Rolling On
  • 241
  • The idea
  • 241
  • The rolling map
  • 241
  • The orthonormal frame bundle
  • 243
  • Species-area curves
  • Extending the rolling map
  • 245
  • Lecture 3.
  • About Wm
  • 253
  • Martingale properties
  • 253
  • Fun and games with Bochner's identity
  • 256
  • Lecture 4.
  • 20
  • A Few Facts, and Something Else
  • 261
  • H[superscript 1] ([0, [infinity]); M) as a Riemannian manifold
  • 261
  • An affine connection and its geodesics
  • 263
  • Perturbing paths along geodesics and Driver's formula
  • 265
  • Some comments and extensions
  • 270
  • Stochastic Spatial Models
  • Species abundance distributions
  • Analysis on Path and Loop Spaces
  • Elton P. Hsu
  • 277
  • Lecture 1.
  • Euclidean Brownian Motion
  • 281
  • Definition of euclidean Brownian motion
  • 281
  • Basic properties
  • 283
  • 22
  • Quasi-invariance of the Wiener measure
  • 284
  • Brownian bridge
  • 285
  • Quasi-invariance of the Wiener measure in loop space
  • 287
  • Lecture 2.
  • Gradient Operator
  • 291
  • Gradient operator
  • Local limit theorems
  • 291
  • Integration by parts
  • 293
  • Closability of the gradient operator
  • 295
  • Gradient operator in flat loop space
  • 296
  • Lecture 3.
  • Ornstein-Uhlenbeck Operator
  • 299
  • 23
  • Definition and basic properties
  • 299
  • Spectrum of the Ornstein-Uhlenbeck operator
  • 301
  • Logarithmic Sobolev inequality
  • 304
  • Hypercontractivity of the Ornstein-Uhlenbeck semigroup
  • 305
  • Lecture 4.
  • Brownian Motion on Manifolds
  • Lecture 4.
  • 309
  • Preliminaries
  • 309
  • Construction of Riemannian Brownian motion
  • 311
  • Horizontal lift of Brownian motion
  • 313
  • Lecture 5.
  • Gradient Formulas
  • 319
  • The Block Construction
  • A commutation relation
  • 319
  • Gradient formula I
  • 321
  • Gradient formula II
  • 323
  • Bismut's formula for the gradient of the heat kernel
  • 324
  • Lecture 6.
  • Integration by Parts
  • 27
  • 325
  • Gradient operator in the path space
  • 325
  • Integration by parts in path space
  • 327
  • Brownian bridge on Riemannian manifolds
  • 329
  • Integration by parts in the loop space
  • 331
  • Lecture 7.
  • Oriented percolation
  • Logarithmic Sobolev Inequalities
  • 337
  • Martingale representation theorem
  • 337
  • Proof of the main result
  • 339
  • Generalized Ornstein-Uhlenbeck operator
  • 341
  • An Introduction to Option Pricing and the Mathematical Theory of Risk
  • Marco Avellaneda
  • 27
  • 349
  • Investments and probability
  • 352
  • Options
  • 354
  • Risk-neutral probabilities
  • 358
  • Risk-management using the "Greeks"
  • 361
  • Uncertain volatility models
  • The stability theorem of Gray and Griffeath
  • 365
  • Relative entropy: combining volatility uncertainty with a-priori beliefs
  • 369
  • Rick Durrett
  • 30
  • Lecture 5.
  • Long Range Limits
  • 35
  • Estimation for the limit system
  • 37
  • Continuity argument
  • 37
  • Lecture 6.
  • Rapid Stirring Limits
  • 5
  • 39
  • Independent and Dependent Percolation
  • Jennifer Tour Chayes, Amber L. Puha, Ted Sweet
  • 49
  • Lecture 1.
  • The Basics of Percolation
  • 53
  • Relevant quantities and expected behavior
  • 53
  • Basic techniques
  • Lecture 1.
  • 62
  • Lecture 2.
  • Rescaling and Finite-Size Scaling in Percolation
  • 67
  • Rescaling and characterization of phases (d = 2)
  • 67
  • Finite-size scaling and the correlation length
  • 72
  • Lecture 3.
  • Critical Exponent Inequalities
  • The Voter Model
  • 81
  • A bound on the correlation length via finite-size scaling events
  • 81
  • Mean-field bounds
  • 86
  • Lecture 4.
  • Two Fundamental Questions
  • 93
  • Absence of an intermediate phase
  • 93
  • 9
  • Uniqueness of the infinite cluster
  • 99
  • Lecture 5.
  • Finite-Size Scaling and the Incipient Infinite Cluster
  • 105
  • The motivation
  • 105
  • Definitions of relevant quantities and preliminaries
  • 108
  • The scaling axioms and the results
  • Construction and duality
  • 111
  • Interpretation of the results
  • 117
  • Lecture 6.
  • The BK(R) Inequality
  • 119
  • Equivalent forms of the inequality
  • 119
  • Preliminaries to the proof of the BK inequality
  • 121
  • 9
  • The proof of the BK inequality
  • 122
  • Lecture 7.
  • The Potts Model and the Random Cluster Model
  • 129
  • The Potts models
  • 130
  • The Fortuin-Kasteleyn representation
  • 134
  • Standard correlation inequalities
Control code
40359464
Dimensions
27 cm
Extent
x, 374 pages
Isbn
9780821805909
Isbn Type
(hc. : alk. paper)
Lccn
98051767
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)40359464

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