<a href="https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.pdf">High-Dimensional Probability(PDF)</a>
The following figure is particularly impressive and is often mentioned
<img src="https://gyazo.com/dcf7797f57cd32ab019fbd0396646b33/thumb/1000" alt="image">
<ul>
<li>In <a href="/en/high-dimensional%20space">high-dimensional space</a>, the <a href="/en/normal%20distribution">normal distribution</a> is approximately the <a href="/en/uniform%20distribution">uniform distribution</a> on the [hypersphere</li>
</ul>
<img src="https://gyazo.com/333f9a1fe466097b2447849eba7a73d9/thumb/1000" alt="image">
<img src="https://gyazo.com/bfb9b32688c26d8deacb4e94ddd8536b/thumb/1000" alt="image">
relevance
- <a href="/en/Distance%20of%20high-dimensional%20normal%20distribution%20has%20mean%20%E2%88%9AD%2C%20variance%200.7">Distance of high-dimensional normal distribution has mean √D, variance 0.7</a>
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In high-dimensional space, the normal distribution is almost uniformly distributed on the hypersphere