Let's consider the thermal noise (or Johnson–Nyquist noise): It is white noise, that means that its power spectral density does not depend on frequency.
Now my question is: Which is a typical time domain graph of this noise? From a mathematical point of view, I'd say it is a $\delta(t)$, since power spectral density = constant means Fourier Transform = constant, that means signal in time domain = $\delta(t)$.
But physically it is difficult for me to understand it. I'd say that thermal noise is a series of random fluctuations, like this one (and this is the behaviour that can be also found on the web):