Timeline for connection between the Gaussian and the Cauchy distribution
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Oct 4 at 19:11 | comment | added | Michael Hardy | I'm surprised that you would say you can't see why the angle is uniformly distributed just after you said the distribution is rotationally symmetric. Look at it like this: Instead of that one line that is one unit away from the starting point of the Brownian motion, think of all lines at that same distance from the starting point. The probability distribution should be the same for all of them, because of the rotational symmetry. So the angle is uniformly distributed. | |
| Aug 6, 2010 at 10:40 | history | edited | Robin Chapman | CC BY-SA 2.5 |
added content
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| Aug 6, 2010 at 10:27 | comment | added | Tracy Hall | In fact, the Gaussian distribution is, up to scaling, the unique distribution such that an independent product is rotationally invariant, and can be derived from that characterization. This is equivalent to the mysterious fact that a random walk on a rectangular grid renormalizes to something anisotropic; somehow the grid axes disappear. | |
| Aug 6, 2010 at 9:33 | history | edited | Robin Chapman | CC BY-SA 2.5 |
removed dubious statement
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| Aug 6, 2010 at 8:37 | history | answered | Robin Chapman | CC BY-SA 2.5 |