The Library
Symmetries and zero modes in sample path large deviations
Tools
Tools
Tools
Schorlepp, Timo, Grafke, Tobias and Grauer, Rainer (2023) Symmetries and zero modes in sample path large deviations. Journal of Statistical Physics, 190 . 50. doi:10.1007/s10955-022-03051-w ISSN 0022-4715.
|
PDF
WRAP-symmetries-zero-modes-sample-path-large-deviations-Grafke-2022.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (1492Kb) | Preview |
|
![[img]](https://wrap.warwick.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
WRAP-symmetries-zero-modes-sample-path-large-deviations-Grafke-2022.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (2116Kb) |
Official URL: https://doi.org/10.1007/s10955-022-03051-w
Abstract
Sharp large deviation estimates for stochastic differential equations with small noise, based on minimizing the Freidlin-Wentzell action functional under appropriate boundary conditions, can be obtained by integrating certain matrix Riccati differential equations along the large deviation minimizers or instantons, either forward or backward in time. Previous works in this direction often rely on the existence of isolated minimizers with positive definite second variation. By adopting techniques from field theory and explicitly evaluating the large deviation prefactors as functional determinant ratios using Forman’s theorem, we extend the approach to general systems where degenerate submanifolds of minimizers exist. The key technique for this is a boundary-type regularization of the second variation operator. This extension is particularly relevant if the system possesses continuous symmetries that are broken by the instantons. We find that removing the vanishing eigenvalues associated with the zero modes is possible within the Riccati formulation and amounts to modifying the initial or final conditions and evaluation of the Riccati matrices. We apply our results in multiple examples including a dynamical phase transition for the average surface height in short-time large deviations of the one-dimensional Kardar-Parisi-Zhang equation with flat initial profile.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Journal or Publication Title: | Journal of Statistical Physics | ||||||
| Publisher: | Springer New York LLC | ||||||
| ISSN: | 0022-4715 | ||||||
| Official Date: | 9 January 2023 | ||||||
| Dates: |
|
||||||
| Volume: | 190 | ||||||
| Article Number: | 50 | ||||||
| DOI: | 10.1007/s10955-022-03051-w | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 14 December 2022 | ||||||
| Date of first compliant Open Access: | 18 January 2023 | ||||||
| Funder: | T.S. and R.G. benefited from support through the DFG collaborative research center SFB-1491. T.G. acknowledges the support received from the EPSRC projects EP/T011866/1 and EP/V013319/1 |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
