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Large deviations for the macroscopic motion of an interface

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Version 2 2023-06-13, 15:03
Version 1 2023-06-09, 04:38
journal contribution
posted on 2023-06-13, 15:03 authored by P Birmpa, N Dirr, D Tsagkarogiannis
We study the most probable way an interface moves on a macroscopic scale from an initial to a final position within a fixed time in the context of large deviations for a stochastic microscopic lattice system of Ising spins with Kac interaction evolving in time according to Glauber (non-conservative) dynamics. Such interfaces separate two stable phases of a ferromagnetic system and in the macroscopic scale are represented by sharp transitions. We derive quantitative estimates for the upper and the lower bound of the cost functional that penalizes all possible deviations and obtain explicit error terms which are valid also in the macroscopic scale. Furthermore, using the result of a companion paper about the minimizers of this cost functional for the macroscopic motion of the interface in a fixed time, we prove that the probability of such events can concentrate on nucleations should the transition happen fast enough.

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of Statistical Physics

ISSN

0022-4715

Publisher

Springer Verlag

Issue

5

Volume

166

Page range

1163-1192

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-01-11

First Open Access (FOA) Date

2017-02-27

First Compliant Deposit (FCD) Date

2017-01-11

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