# Why different noise terms are read at specific sampling interval in Allan Variance plot?

I was trying to identify Quantization Noise, Angle Random Walk, Bias Instability, and Rate Random Walk from Allan Variance plot which as Allan deviation on y axis and Sampling Time Interval T on x axis. Several sources [1][2] say that we can read these values directly from the plot when T=3^1/2, T=1, Slope=0, T=3 respectively. I am trying to understand why is this the case.

Here is my understanding: Allan Variance (AVAR) plot is generated by calculating AVAR at different sampling intervals T. Different noise processes have different slopes and they appear in different regions of T. Now, "its empirical observation" (and there is no mathematical proof as such) that Allan Variance plot is sensitive to different noise process at different sampling intervals T. For example, Allan Variance plot is sensitive to random walk component at T=3, while sensitive to white noise component for T=1. Thats why we simply read y axis deviation values for these different x axis T values to obtain corresponding values for these different noise processes.

Am I correct with this? That is this mapping of noise processes to different values of T is purely based on empirical observation of how these noises appear in sensors?