The geometrical meaning of statistical isotropy of smooth random fields in two dimensions
Pravabati Chingangbam,
Priya Goyal,
K. P. Yogendran
et al.
Abstract:We revisit the geometrical meaning of statistical isotropy that is manifest in excursion sets of smooth random fields in two dimensions. Using the contour Minkowski tensor, W1, as our basic tool we first examine geometrical properties of single structures. For simple closed curves in two dimensions we show that W1 is proportional to the identity matrix if the curve has m-fold symmetry, with m ≥ 3. Then we elaborate on how W1 maps any arbitrary shaped simple closed curve to an ellipse that is unique up to trans… Show more
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