Gel'fand-Yaglom type equations for calculating fluctuations around Instantons in stochastic systems
| Autor: | Timo Schorlepp, Rainer Grauer, Tobias Grafke |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Instanton Dynamical systems theory Discretization Gaussian General Physics and Astronomy FOS: Physical sciences Probability density function 01 natural sciences 010305 fluids & plasmas symbols.namesake Matrix (mathematics) 0103 physical sciences Statistical physics 010306 general physics QA Mathematical Physics QC Condensed Matter - Statistical Mechanics Mathematics Statistical Mechanics (cond-mat.stat-mech) Fluid Dynamics (physics.flu-dyn) Statistical and Nonlinear Physics Physics - Fluid Dynamics Modeling and Simulation Path integral formulation symbols Large deviations theory |
| ISSN: | 1751-8113 |
| Popis: | In recent years, instanton calculus has successfully been employed to estimate tail probabilities of rare events in various stochastic dynamical systems. Without further corrections, however, these estimates can only capture the exponential scaling. In this paper, we derive a general, closed form expression for the leading prefactor contribution of the fluctuations around the instanton trajectory for the computation of probability density functions of general observables. The key technique is applying the Gel'fand-Yaglom recursive evaluation method to the suitably discretized Gaussian path integral of the fluctuations, in order to obtain matrix evolution equations that yield the fluctuation determinant. We demonstrate agreement between these predictions and direct sampling for examples motivated from turbulence theory. 27 pages, 5 figures |
| Databáze: | OpenAIRE |
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