most citedThe expected area of the filled planar Brownian loop is Pi/5

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math.PR2005★ 28 cited

The expected area of the filled planar Brownian loop is Pi/5

Christophe Garban, José A. Trujillo Ferreras

Let B_t be a planar Brownian loop of time duration 1 (a Brownian motion conditioned so that B_0 = B_1). We consider the compact hull obtained by filling in all the holes, i.e. the…