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The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime

Anderson, Johan and Johansson, Jonas LU (2016) In Journal of Physics A: Mathematical and Theoretical 49(50).
Abstract

An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a Tracy-Widom distribution i.e. a PDF tail proportional to exp (cw2 3/2), Where w 2 is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin-Siggia-Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution... (More)

An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a Tracy-Widom distribution i.e. a PDF tail proportional to exp (cw2 3/2), Where w 2 is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin-Siggia-Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no upper critical dimension.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
instanton, KPZ, non-linear system, PDF
in
Journal of Physics A: Mathematical and Theoretical
volume
49
issue
50
publisher
IOP Publishing
external identifiers
  • scopus:84999723713
  • wos:000389175800001
ISSN
1751-8113
DOI
10.1088/1751-8113/49/50/505001
language
English
LU publication?
yes
id
1a67f570-61b4-49fb-aa76-f15a62111fa9
date added to LUP
2016-12-19 09:47:13
date last changed
2017-09-18 11:32:04
@article{1a67f570-61b4-49fb-aa76-f15a62111fa9,
  abstract     = {<p>An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a Tracy-Widom distribution i.e. a PDF tail proportional to exp (cw<sub>2</sub> <sup>3/2</sup>), Where w <sub>2</sub> is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin-Siggia-Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no upper critical dimension.</p>},
  articleno    = {505001},
  author       = {Anderson, Johan and Johansson, Jonas},
  issn         = {1751-8113},
  keyword      = {instanton,KPZ,non-linear system,PDF},
  language     = {eng},
  month        = {11},
  number       = {50},
  publisher    = {IOP Publishing},
  series       = {Journal of Physics A: Mathematical and Theoretical},
  title        = {The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime},
  url          = {http://dx.doi.org/10.1088/1751-8113/49/50/505001},
  volume       = {49},
  year         = {2016},
}