Course-graining – how we simplify the system by the aggregation of parts.
Effective theory – what our new description of the system looks like when we coarse-grain.
Basin of attraction – which other mechanistic stories turn into the same effective theory.
Central limit theorem – the distribution of a sum of independent, identically-distributed variables, where the underlying distribution has finite variance, tends towards a Gaussian.

We have a fine-grained description of a random walk, which tracks the exact sequence of steps that we take. And we have a coarse-grained description, which cares only about the final displacement.

Standard deviation scales as $\sqrt{n}$ (square root of the sample size).

1. The mean of a sum of random variables is equal to the sum of the individual means.
2. The variance of a sum of independent random variables is equal to the sum of the individual variances.

Universality – the idea that many different microscopic models can give rise to the same macroscopic behavior.