On the expected diameter of planar Brownian motion
Abstract
Known results show that the diameter d1 of the trace of planar Brownian motion run for unit time satisfies 1.595 ≤ E d1 ≤ 2.507. This note improves these bounds to 1.601 ≤ E d1 ≤ 2.355. Simulations suggest that E d1 ≈ 1.99.
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