Mathelirium(@mathelirium):The High-Dimensional Ball Is Full, but Its Probability Mass Lives Near the Boundary High-dimensional probability is weird. As the dimension grows, a uniform point in the ball does not usually land deep inside. Most of the mass gets pushed into a very thin shell near the boundary.

Mathelirium

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My work sits at the intersection of Applied Mathematics, Computational Physics, Scientific Visualization, and Technical Storytelling.

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Mathelirium@mathelirium

2026.04.07 11:56

The High-Dimensional Ball Is Full, but Its Probability Mass Lives Near the Boundary High-dimensional probability is weird. As the dimension grows, a uniform point in the ball does not usually land deep inside. Most of the mass gets pushed into a very thin shell near the boundary.