Or just draw a straight line from one end of the walk to the other. Maybe exclude cases where this line intersects the path-so-far. Rich --- Quoting meekerdb <meekerdb@verizon.net>:
On 12/24/2012 4:47 PM, Fred lunnon wrote:
On 12/25/12, Bill Gosper<billgosper@gmail.com> wrote:
Awful thought: What is the expected time at which a 3D random walk first becomes "knotted"? (W.r.t. pulling on the ends.) Bearing in mind that the ends may in general lie deep within the convex hull of the walk, perhaps this question requires rather more careful definition ... WFL
You could constrain the question to those random walks that return to the starting point (although of measure zero) or you could try defining a different kind of 'random walk' that starts with a unit loop and randomly expands and rearranges it, with crossovers allowed.
Brent
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