Marc Raimondo - CMI

Orthogonal Case
P { max
1≤j≤N+1 xj ≤ x0} = � det(I − KN+1χ0),
⎛ ⎞ ⎛ ⎞
I
KN+1(x,y) = ⎝
ǫ1
−∂2
0 0
⎠SN+1,1(x,y) − ⎝ ⎠
T
ǫ(x − y) 0
∂2 ↔ ∂/∂y
ǫ1 ↔ convolution in x with ǫ(x) = 1
2 sgn(x)
T ↔ transpose x,y
Key identity relates orthogonal at N + 1 to unitary at N :
SN+1,1(x,y) = SN,2(x,y) + 1
2 φ(x)ǫψ(y).
Luminy 12/08 – p.40