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Persistence of the Wiener sausage: sampling stability and limit theorems for Betti-curve functionals of planar Brownian motion
We study the persistent homology of the offset filtration generated by the range of a planar Brownian motion with constant nonzero drift (Wiener sausages of increasing radius). We prove what are, to our knowledge, the first law of large numbers and central limit theorem for its smoothed Betti-curve
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