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Large deviations for the macroscopic motion of an interface
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 TsagkarogiannisWe 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 PhysicsISSN
0022-4715Publisher
Springer VerlagExternal DOI
Issue
5Volume
166Page range
1163-1192Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-01-11First Open Access (FOA) Date
2017-02-27First Compliant Deposit (FCD) Date
2017-01-11Usage metrics
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