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Tuesday, 30 January 2018: Joint ACiD/NODES Seminar

Andrew Wade (Durham, Maths): Convex hulls of random walks

Time and Location:

13:00 in E360 (Durham)

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On each of n unsteady steps, a drunken gardener drops a seed. Once the flowers have bloomed, what is the minimum length of fencing required to enclose the garden? What is its area? I will describe recent work on the convex hull of planar random walk, concerned in particular with the large-n asymptotics of its perimeter length and area. We provide variance asymptotics and distributional limit theorems. Of the four combinations of the two quantities (perimeter and area) in the two regimes (zero drift or non-zero drift for the steps of the walk), one limit is Gaussian; three are not. This talk is mostly based on joint work with Chang Xu (Strathclyde); I’ll also mention ongoing work with Ostap Hryniv and James McRedmond (Durham).