Softcover ISBN: | 978-2-85629-973-9 |
Product Code: | AST/441 |
List Price: | $57.00 |
AMS Member Price: | $45.60 |
Softcover ISBN: | 978-2-85629-973-9 |
Product Code: | AST/441 |
List Price: | $57.00 |
AMS Member Price: | $45.60 |
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Book DetailsAstérisqueVolume: 441; 2023; 119 ppMSC: Primary 82; 60
Many models of one-dimensional local random growth are expected to lie in the Kardar-Parisi-Zhang (KPZ) universality class. For such a model, the interface profile in the long time limit is expected—and proved for a few integrable models—to be, when viewed in appropriately scaled coordinates, up to a parabolic shift, the \(\mathrm{Airy}_{2}\) process \(\mathcal{A}: \mathbb{R} \to \mathbb{R}\). This process may be embedded via the Robinson-Schensted-Knuth correspondence as the uppermost curve in an \(\mathbb{N}\)-indexed system of random continuous curves, the Airy line ensemble.
Among the authors' principal results is the assertion that the \(\mathrm{Airy}_{2}\) process enjoys a very strong similarity to Brownian motion (of rate two) on unit-order intervals.
The authors' technique of proof harnesses a probabilistic resampling or Brownian Gibbs property satisfied by the Airy line ensemble after parabolic shift, and this book develops Brownian Gibbs analysis of this ensemble begun in the work of Corwin and Hammond (2014) and pursued by Hammond (2019).
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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Many models of one-dimensional local random growth are expected to lie in the Kardar-Parisi-Zhang (KPZ) universality class. For such a model, the interface profile in the long time limit is expected—and proved for a few integrable models—to be, when viewed in appropriately scaled coordinates, up to a parabolic shift, the \(\mathrm{Airy}_{2}\) process \(\mathcal{A}: \mathbb{R} \to \mathbb{R}\). This process may be embedded via the Robinson-Schensted-Knuth correspondence as the uppermost curve in an \(\mathbb{N}\)-indexed system of random continuous curves, the Airy line ensemble.
Among the authors' principal results is the assertion that the \(\mathrm{Airy}_{2}\) process enjoys a very strong similarity to Brownian motion (of rate two) on unit-order intervals.
The authors' technique of proof harnesses a probabilistic resampling or Brownian Gibbs property satisfied by the Airy line ensemble after parabolic shift, and this book develops Brownian Gibbs analysis of this ensemble begun in the work of Corwin and Hammond (2014) and pursued by Hammond (2019).
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.