Typical representatives of free homotopy classes in multi-punctured plane
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We show that a uniform probability measure supported on a specific set of piecewise linear loops in a nontrivial free homotopy class in a multi-punctured plane is overwhelmingly concentrated around loops of minimal lengths. Our approach is based on extending Mogulskii’s theorem to closed paths, which is a useful result of independent interest. In addition, we show that the above measure can be sampled using standard Markov Chain Monte Carlo techniques, thus providing a simple method for approximating shortest loops.
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2014 ◽
Vol 30
(4)
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pp. 300-316
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2019 ◽
Vol 15
(5)
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pp. 1115-1126
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2015 ◽
Vol 24
(6)
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pp. 566-579
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