Say I want to generate a random number $x\in [0, 128^{64}]$ with the expected value being 64. The trivial answer seems to be to roll a random vector $v = [0,1)^{128^{64}}$ with the answer then being $x=|\{n\in [1, 128^{64}]|v_n<(\frac{64}{128^{64}})\}|$. Now obviously generating $128^{64}$ random numbers isn't exactly computationally feasible. Obviously there are many alternate distributions or just approximations but for the sake of the argument let's say I want exactly that binomial distribution.
Is there another way to roll such a random number without it being too computationally intensive?
I understand that this question might be understood as a computer science problem, but for now I'm more interested in learning about alternate ways to generate random variates like this.
I tried playing around with the quantile function of the binomial distribution and then rolling a uniform random number on the domain of that function, but I didn't get anywhere.
As $p=\frac{64}{128^{64}}=2^{-442}$ is insanely low, I think you can consider your random variable as a constant. If you really want to experiment, simulate a Poisson variable with this parameter.