Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

An Eyring–Kramers law for the stochastic Allen–Cahn equation in dimension two

Tools
- Tools
+ Tools

Berglund, Nils, Di Gesù, Giacomo and Weber, Hendrik (2017) An Eyring–Kramers law for the stochastic Allen–Cahn equation in dimension two. Electronic Journal of Probability, 22 . 41. doi:10.1214/17-EJP60

[img]
Preview
PDF
WRAP-Eyring–Kramers-law-stochastic-Weber-2017.pdf - Published Version - Requires a PDF viewer.
Available under License Creative Commons Attribution 2.0..

Download (799Kb) | Preview
[img] PDF
1604.05742.pd.pdf - Accepted Version
Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer.

Download (337Kb)
Official URL: http://dx.doi.org/10.1214/17-EJP60

Request Changes to record.

Abstract

We study spectral Galerkin approximations of an Allen–Cahn equation over the two-dimensional torus perturbed by weak space-time white noise of strength ε√ε. We introduce a Wick renormalisation of the equation in order to have a system that is well-defined as the regularisation is removed. We show sharp upper and lower bounds on the transition times from a neighbourhood of the stable configuration −1−1 to the stable configuration 11 in the asymptotic regime ε→0ε→0. These estimates are uniform in the discretisation parameter NN, suggesting an Eyring–Kramers formula for the limiting renormalised stochastic PDE. The effect of the “infinite renormalisation” is to modify the prefactor and to replace the ratio of determinants in the finite-dimensional Eyring–Kramers law by a renormalised Carleman–Fredholm determinant.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Stochastic partial differential equations, Potential theory (Physics), Galerkin methods
Journal or Publication Title: Electronic Journal of Probability
Publisher: University of Washington. Dept. of Mathematics
ISSN: 1083-6489
Official Date: 28 April 2017
Dates:
DateEvent
28 April 2017Published
23 April 2017Accepted
Volume: 22
Article Number: 41
DOI: 10.1214/17-EJP60
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
Funder: European Research Council (ERC), Seventh Framework Programme (European Commission) (FP7), Engineering and Physical Sciences Research Council (EPSRC), Royal Society (Great Britain). University Research Fellowship
Grant number: (FP/2007-2013) / ERC Grant Agreement number 614492 (ERC) (FP7)

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item
twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us