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

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

Statement of responsibility

Elton P. Hsu, S.R.S. Varadhan, editors

Instantiates

• Probability theory and applications

Publication

• Providence, R.I., American Mathematical Society | Institute for Advanced Study, ©1999

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)

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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

Record ID

.b41809701

System control number

(OCoLC)40359464