content_image/304603.jpg content_image/304602.jpg content_image/304601.jpg
where δ$_{js}$ = 1 { j = s } stands for the classical Kronecker symbol. As will be shown below, after an appropriate change of measure, γ ( j,s ) p 1 and γ ( j,s ) p 2 are asymptotically centered Gaussian. Expressing the exponent in (22) as a function of γ ( j,s ) p 1 and γ ( j,s ) p 2 , changing the measure of integration, and using the asymptotic Gaussianity will establish the proposition. 

Let γ$_{p}$ = ( γ (1 , 1) p , ..., γ ( r, 1) p , γ (2 , 2) p , ..., γ ( r, 2) p , γ (3 , 3) p , ..., γ ( r,r ) p ′$_{, where}$ γ ( j,s ) p = ( γ ( j,s ) p 1 , γ ( j,s ) p 2 ) . Using this notation, (22), (23), and (24), we get, after some algebra, 

<img src='content_image/304603.jpg'>

where is the standard Gaussian probability measure, and 

<img src='content_image/304602.jpg'>

where G ( j ) pi is a ( j − 1) × ( j − 1) matrix with ( k, s )-th element p − 1 / $^{2}$γ ( k,s ) pi , 

Next, define the event 

<img src='content_image/304601.jpg'>

B$_{M,M}$$_{′}$ = {∣ ∣ γ ( j,s ) p 1 ∣ ≤ M and ∣ γ ( j,s ) p 2 ∣ ≤ $_{M}$′ for all j, s = 1 , ..., r } , where M and M ′ are positive parameters to be specified later. Somewhat abusing notation, we will also refer to B$_{M,M}$$_{′}$ as a rectangular region in R r $^{2}$+ r that consists 

