Concentration properties of Gaussian random fields
Abstract
We study the problem of a random Gaussian vector field given that a particular real quadratic form $\mathcal{Q}$ is arbitrarily large. We prove that in such a case the Gaussian field is primarily governed by the fundamental eigenmode of a particular operator. As a good check of our proposition we use it to rederive the result of Adler dealing with the structure of field in the vicinity of a high local maxima. We have also applied our result to an incompressible homogeneous Gaussian random flow in the limit of large local helicity and calculate the structure of the flow.
 Publication:

arXiv eprints
 Pub Date:
 April 2014
 DOI:
 10.48550/arXiv.1404.7424
 arXiv:
 arXiv:1404.7424
 Bibcode:
 2014arXiv1404.7424S
 Keywords:

 Mathematical Physics;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 M2 Thesis 2012, \'{E}cole Polyechnique, France