In this video, we try to gain some intuition for why symmetric random walks are recurrent in 1 and 2D, but transient in 3D. This was proved by mathematician George Pólya in 1921.
Links for further reading:
Awesome demos of random walks by Russell Lyons ([ Ссылка ])
Analysis of high-dimensional random walks by Gregory Lawler, including expected escape time ([ Ссылка ])
Lecture on random walks by Andrej Košmrlj, including some physics and biology connections ([ Ссылка ])
Special thanks to Ryan Adams, Elmira Amirloo, Alex Beatson, and Yair Shenfeld for feedback on this video.
Some of the animations in this video were created with 3Blue1Brown's manim library ([ Ссылка ]).
Music: Trinkets by Vincent Rubinetti
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