Some remarks on mutual windings
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Séminaire de probabilités de Strasbourg
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Frank B. Knight (1993)
Séminaire de probabilités de Strasbourg
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Thomas S. Mountford (1993)
Séminaire de probabilités de Strasbourg
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Séminaire de probabilités de Strasbourg
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Séminaire de probabilités de Strasbourg
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Séminaire de probabilités de Strasbourg
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Krzysztof Burdzy, Davar Khoshnevisan (1995)
Séminaire de probabilités de Strasbourg
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Séminaire de probabilités de Strasbourg
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Journal of the European Mathematical Society
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We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that is, this process is ballistic and has an asymptotic velocity approximately 4.58... as high as required by the conditioning (the exact value of this constant involves the first zero of a Bessel function). We also study the random walk case and show...