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I was wondering if there are any papers out there that study the following 2D random walk situation:

1) Start a random walk at the origin

2) Once the walk forms a loop, stop the walk and "remove the tail"

After these two steps you are left with the loop. I'm interested in any results that look at the geometric properties of this loop, and if such a loop occurs in finite time, etc.

Thanks for your time!

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