- #1
CuppoJava
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Homework Statement
Show that:
p(r'+e) [tex]\cong[/tex] p(r')*exp( -3e2 / 2s2 ) for large D
given that:
p(r) = rD-1 * exp( -r2 / 2s2 )
r' = sqrt(D) * s
Homework Equations
This arises out of a D-dimensional gaussian distribution and r' is the radius at which the probability is maximized.
The Attempt at a Solution
I've gotten to the point:
p(r'+e) [tex]\propto[/tex] exp( -(r'+e)2 / 2s2 + (D-1)ln(r'+e) )
And the solution manual says that using the Taylor expansion for ln, will help everything reduce down, but all I get is a mess. What really baffles me is where the dependence on D went.
Thanks very much for your help
-Patrick