High Dimensional Probability

High-dimensional probability studies how random phenomena behave in spaces with many variables or dimensions, often much more than our usual 3D world. As dimensions increase, our intuition can be misleading—points tend to be far apart, and data can concentrate in unexpected ways. This field helps us understand the likelihood of events in complex systems like large networks, machine learning models, or data with dozens or hundreds of features. It provides tools to analyze and predict outcomes where traditional probability ideas may not apply directly, revealing patterns and structures hidden in high-dimensional settings.