For Gaussian fields with variance loss 1-σ(t) ~ t1^β + t2^β + t1^a t2^a near the corner maximum, when a < β/2 the leading contribution to high excursions shifts from the classical rectangle to side-attached or effectively one-dimensional regions, producing new logarithmic and side-dominated asymptot
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Extremes of Gaussian fields with a product term in the variance
For Gaussian fields with variance loss 1-σ(t) ~ t1^β + t2^β + t1^a t2^a near the corner maximum, when a < β/2 the leading contribution to high excursions shifts from the classical rectangle to side-attached or effectively one-dimensional regions, producing new logarithmic and side-dominated asymptot