Stationary Phase Method with Estimate of Remainder Term over a Space of Large Dimension

Abstract

Let $r_d(\nu)$ denote the remainder term of the stationary phase method over $R^d$. Then an estimate of $\nu^{d/2+1}r_d(\nu)$, as $d \to \infty$, is given under certain assumptions, which are tolerable for application to Feynman path integrals.