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Sample-path large deviations for stochastic evolutions driven by the square of a Gaussian process
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Bouchet, Freddy, Tribe, Roger and Zaboronski, Oleg V. (2023) Sample-path large deviations for stochastic evolutions driven by the square of a Gaussian process. Physical Review E, 107 (3). 034111. doi:10.1103/PhysRevE.107.034111 ISSN 1539-3755.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.107.034111
Abstract
Recently, a number of physical models have emerged described by a random process with increments given by a quadratic form of a fast Gaussian process. We find that the rate function which describes sample-path large deviations for such a process can be computed from the large domain size asymptotic of a certain Fredholm determinant. The latter can be evaluated analytically using a theorem of Widom which generalizes the celebrated Szegő-Kac formula to the multidimensional case. This provides a large class of random dynamical systems with timescale separation for which an explicit sample-path large-deviation functional can be found. Inspired by problems in hydrodynamics and atmosphere dynamics, we construct a simple example with a single slow degree of freedom driven by the square of a fast multivariate Gaussian process and analyze its large-deviation functional using our general results. Even though the noiseless limit of this example has a single fixed point, the corresponding large-deviation effective potential has multiple fixed points. In other words, it is the addition of noise that leads to metastability. We use the explicit answers for the rate function to construct instanton trajectories connecting the metastable states.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Gaussian processes, Stochastic processes -- Mathematical models, Markov processes, Probabilities -- Mathematical models | ||||||
Journal or Publication Title: | Physical Review E | ||||||
Publisher: | American Physical Society | ||||||
ISSN: | 1539-3755 | ||||||
Official Date: | 7 March 2023 | ||||||
Dates: |
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Volume: | 107 | ||||||
Number: | 3 | ||||||
Number of Pages: | 12 | ||||||
Article Number: | 034111 | ||||||
DOI: | 10.1103/PhysRevE.107.034111 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Copyright Holders: | American Physical Society | ||||||
Date of first compliant deposit: | 27 March 2023 | ||||||
Date of first compliant Open Access: | 27 March 2023 | ||||||
Open Access Version: |
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