2014/04/29 by Sharma, Gargee
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1404.7424
We study the problem of a random Gaussian vector field given that a particular real quadratic form 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 re-derive 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.