uniform random unit vector: Y=(Yi,,Y,Y+1,.,Ya) Let =(Yi,...,Yk) with probability o(&） 1zP> or IlZ1<2d d Looks clean,however... ●‖ZI2=Y+Y好+…+Y Yi's are dependent for uniform unit vector Y
with probability o( 1 Z = (Y1,...,Yk) n2 ) Z2 > 3k 2d Z2 < k 2d or Y = (Y1,...,Yk, Yk+1,...,Yd) Let Looks clean, however . . . • • ⇥Z⇥2 = Y 2 1 + Y 2 2 + ··· + Y 2 k Yi’s are dependent for uniform unit vector Y . uniform random unit vector:
uniform random unit vector: Y=(Yi,,Y,Y+1,.,Ya) Let =(Yi,...,Yk) with probability o(是） W22> k 2d or Z2< Step III: Bound‖Z2
with probability o( 1 Z = (Y1,...,Yk) n2 ) Z2 > 3k 2d Z2 < k 2d or Y = (Y1,...,Yk, Yk+1,...,Yd) Let Step III: Bound Z . 2 uniform random unit vector: