Testing the Instanton Approach to the Large Amplification Limit of a Diffraction-Amplification Problem
Résumé
The validity of the instanton analysis approach is tested numerically in the case of the diffraction-
Here, S(x, z) is a complex Gaussian random field, z and x respectively are the axial and transverse coordinates, with 0 z L, and both m 6 = 0 and g > 0 are real parameters. We consider a class of S, called the 'one-max class', for which we devise a specific biased sampling procedure. As an application, p(U ), the probability distribution of U , is obtained down to values less than 10 2270 in the far right tail. We find that the agreement of our numerical results with the instanton analysis predictions in Mounaix (2023 J. Phys. A: Math. Theor. 56 305001) is remarkable. Both the predicted algebraic tail of p(U ) and concentration of the realizations of S onto the leading instanton are clearly confirmed, which validates the instanton analysis numerically in the large ln U limit for S in the one-max class.
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