On Time Correlations for KPZ Growth in One Dimension
Time correlations for KPZ growth in 1+1 dimensions are reconsidered. We discuss flat, curved, and stationary initial conditions and are interested in the covariance of the height as a function of time at a fixed point on the substrate. In each case the power laws of the covariance for short and long...
Збережено в:
| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147840 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On Time Correlations for KPZ Growth in One Dimension / P.L. Ferrari, H. Spohn // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 50 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1478402019-02-17T01:24:49Z On Time Correlations for KPZ Growth in One Dimension Ferrari, P.L. Spohn, H. Time correlations for KPZ growth in 1+1 dimensions are reconsidered. We discuss flat, curved, and stationary initial conditions and are interested in the covariance of the height as a function of time at a fixed point on the substrate. In each case the power laws of the covariance for short and long times are obtained. They are derived from a variational problem involving two independent Airy processes. For stationary initial conditions we derive an exact formula for the stationary covariance with two approaches: (1) the variational problem and (2) deriving the covariance of the time-integrated current at the origin for the corresponding driven lattice gas. In the stationary case we also derive the large time behavior for the covariance of the height gradients. 2016 Article On Time Correlations for KPZ Growth in One Dimension / P.L. Ferrari, H. Spohn // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 50 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 60K35; 82C22; 82B43 DOI:10.3842/SIGMA.2016.074 http://dspace.nbuv.gov.ua/handle/123456789/147840 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Time correlations for KPZ growth in 1+1 dimensions are reconsidered. We discuss flat, curved, and stationary initial conditions and are interested in the covariance of the height as a function of time at a fixed point on the substrate. In each case the power laws of the covariance for short and long times are obtained. They are derived from a variational problem involving two independent Airy processes. For stationary initial conditions we derive an exact formula for the stationary covariance with two approaches: (1) the variational problem and (2) deriving the covariance of the time-integrated current at the origin for the corresponding driven lattice gas. In the stationary case we also derive the large time behavior for the covariance of the height gradients. |
| format |
Article |
| author |
Ferrari, P.L. Spohn, H. |
| spellingShingle |
Ferrari, P.L. Spohn, H. On Time Correlations for KPZ Growth in One Dimension Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ferrari, P.L. Spohn, H. |
| author_sort |
Ferrari, P.L. |
| title |
On Time Correlations for KPZ Growth in One Dimension |
| title_short |
On Time Correlations for KPZ Growth in One Dimension |
| title_full |
On Time Correlations for KPZ Growth in One Dimension |
| title_fullStr |
On Time Correlations for KPZ Growth in One Dimension |
| title_full_unstemmed |
On Time Correlations for KPZ Growth in One Dimension |
| title_sort |
on time correlations for kpz growth in one dimension |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147840 |
| citation_txt |
On Time Correlations for KPZ Growth in One Dimension / P.L. Ferrari, H. Spohn // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 50 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT ferraripl ontimecorrelationsforkpzgrowthinonedimension AT spohnh ontimecorrelationsforkpzgrowthinonedimension |
| first_indexed |
2023-05-20T17:28:38Z |
| last_indexed |
2023-05-20T17:28:38Z |
| _version_ |
1796153385191211008 |