Concentration of measure

The concentration of measure is a mathematical concept describing how, in high-dimensional spaces, most of the points or outcomes tend to be very close to a certain typical value or average. Think of it as a phenomenon where, as a system becomes more complex or has more degrees of freedom, its behavior becomes more predictable, with random variations shrinking relative to the overall size. This means that in large, complicated systems, there's a high probability that measurements will stay near the average, making exceptional deviations rare. It’s a way to understand stability and predictability in complex, high-dimensional settings.