I'm sampling a DirichletDistribution like so:

>n = 5 000;
>
>par1 = Table[1./n,n];
>
> data1 = RandomVariate[DirichletDistribution[par1],50];  (* This takes about 1.5 seconds *)
>
>par2 = Table[1.,n];
>
> data2 = RandomVariate[DirichletDistribution[par2],50];  (* This takes about 0.10 seconds *)

If I play with the value of the parameters, I find that giving values > 1 radically improves the performance.

Any clues on how to circumvent this?
Thanks!