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Brownian Structure in the KPZ Fixed Point
 
Jacob Calvert University of California, Berkeley, CA
Alan Hammond University of California, Berkeley, CA
Milind Hegde Columbia University, New York, NY
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-973-9
Product Code:  AST/441
List Price: $57.00
AMS Member Price: $45.60
Please note AMS points can not be used for this product
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Brownian Structure in the KPZ Fixed Point
Jacob Calvert University of California, Berkeley, CA
Alan Hammond University of California, Berkeley, CA
Milind Hegde Columbia University, New York, NY
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-973-9
Product Code:  AST/441
List Price: $57.00
AMS Member Price: $45.60
Please note AMS points can not be used for this product
  • Book Details
     
     
    Astérisque
    Volume: 4412023; 119 pp
    MSC: 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.

    Readership

    Graduate students and research mathematicians.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 4412023; 119 pp
MSC: 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.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.