Outputs (3)

The convex hull of a planar random walk: perimeter, diameter, and shape (2018)
Journal Article
McRedmond, J., & Wade, A. R. (2018). The convex hull of a planar random walk: perimeter, diameter, and shape. Electronic Journal of Probability, 23, Article 131. https://doi.org/10.1214/18-ejp257

We study the convex hull of the first n steps of a planar random walk, and present large-n asymptotic results on its perimeter length Ln, diameter Dn, and shape. In the case where the walk has a non-zero mean drift, we show that Ln=Dn ! 2 a.s., and g... Read More about The convex hull of a planar random walk: perimeter, diameter, and shape.

On the centre of mass of a random walk (2018)
Journal Article
Lo, C. H., & Wade, A. R. (2019). On the centre of mass of a random walk. Stochastic Processes and their Applications, 129(11), 4663-4686. https://doi.org/10.1016/j.spa.2018.12.007

For a random walk Sn on Rd we study the asymptotic behaviour of the associated centre of mass process Gn=n−1∑ni=1Si. For lattice distributions we give conditions for a local limit theorem to hold. We prove that if the increments of the walk have zero... Read More about On the centre of mass of a random walk.

A radial invariance principle for non-homogeneous random walks (2018)
Journal Article
Georgiou, N., Mijatović, A., & Wade, A. R. (2018). A radial invariance principle for non-homogeneous random walks. Electronic Communications in Probability, 23, Article 56. https://doi.org/10.1214/18-ecp159

Consider non-homogeneous zero-drift random walks in Rd, d≥2, with the asymptotic increment covariance matrix σ2(u) satisfying u⊤σ2(u)u=U and trσ2(u)=V in all in directions u∈Sd−1 for some positive constants U<V. In this paper we establish weak conver...