How is RMS and Peak-to-peak of white noise calculated
three things to think about:


"white" describes the power spectrum, but to know the peak values, you need to know the probability density function (p.d.f.) of the noise process.  often, with "white noise", we are assuming "normal" or "gaussian" p.d.f.
even for a finite power (which means a finite variance for the p.d.f.), a gaussian random variable has infinite peak value (just that it hits whatever arbitrary high value with decreasing probability).  so for gaussian, you need to define like a "1% likelihood peak value".
true white noise (which does not exist in reality) has infinite power and infinite variance.  this is because true white noise has infinite bandwidth.  so, in reality, we deal with bandlimited "white" noise, so the bandwidth might be a necessary parameter to know, before you can think about its r.m.s. (which is the square root of the variance, assuming no DC component) and peak.