Random walk encircles point with probability zero
Ivars Peterson reports on the Yi Sun's winning project for the Intel Science Talent Search, in which Yi Sun
...worked out the expected number of steps it takes a walker on a two-dimensional grid to encircle a given point (origin). One such circuit corresponds to a winding number of 1.
Yi discovered that the expected number of steps to complete such a circuit in two dimensions is infinite. He also derived an explicit (very complicated) formula for the expected value of the winding number after n steps.
That is a pretty interesting result. The projects for the STS always seem really interesting, which brings me to an ongoing peeve with the STS: the reports are not published in detail anywhere that I have found.
...worked out the expected number of steps it takes a walker on a two-dimensional grid to encircle a given point (origin). One such circuit corresponds to a winding number of 1.
Yi discovered that the expected number of steps to complete such a circuit in two dimensions is infinite. He also derived an explicit (very complicated) formula for the expected value of the winding number after n steps.
That is a pretty interesting result. The projects for the STS always seem really interesting, which brings me to an ongoing peeve with the STS: the reports are not published in detail anywhere that I have found.
posted by db at 5:34 PM
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