For Kraichnan's problem of passive scalar advection by a velocity fiel
d delta correlated in time, the limit of large space dimensionality d
>> 1 is considered. Scaling exponents of the scalar field are analytic
ally found to be zeta(2n) = (n) zeta(2) - 2(2 - zeta(2))n(n - 1)/d, wh
ile those of the dissipation field are mu(n) = -2(2 - zeta(2))n(n - 1)
/d for orders n << d. The refined similarity hypothesis zeta(2n) = n z
eta(2) + mu(n) is thus established by a straightforward calculation fo
r the case considered.