"1/f^a Random Fields, Scaling Properties and Local Averages"
I mainly use the techniques developed in the book, Random Fields: Analysis and Synthesis, by Prof. E. H. VanMarcke to study some properties of the random fields, especially those with 1/f^a spectral densities. I analyzed the scaling properties and fractal structures of the random fields with spectral density 1/f^a and their local averages. I explored the properties of the derivatives of the local-averaged random fields and their relations with the un-averaged ones. I also put forward a generalization of local averages in terms of general response functions.