= Gaussian saddle and endpoint dominance by angle
{c}
{title2=$f(\theta,\lambda)$}
= Gaussian complex-endpoint dominance
{c}
{synonym}
For a <Gaussian integral> from $-1/\sqrt2$ to $e^{i\theta}$, a <saddle point> contribution dominates for $0\leq\theta\leq\pi/4$. The moving <endpoint contribution in steepest descent> dominates for $\pi/4<\theta<5\pi/6$. At $5\pi/6$ the two endpoints have equal exponential rates and both are needed; for larger angles the fixed endpoint dominates. Saddle connectivity switches at $\pi/2$, but that change is subdominant in the leading endpoint regime.
Back to article page
