Estimators of the Correlation Region Area of aЁGaussian Homogeneous Random Field

The notion of correlation region area (CRA) is defined for a homogeneous random field $\{\xi(\mathbf k),\,\mathbf k\in\mathbf Z^2\}$. A statistical estimator is introduced for one of the simplest definitions of CRA. Its asymptotic properties (with sample size increasing to infinity) are investigated for the simplest case where $\xi(\mathbf k)$ is a Gaussian random field with mean $М\xi(\mathbf k)\equiv 0$.