Outputs (3)

Convex hulls of random walks and their scaling limits (2015)
Journal Article
Wade, A. R., & Xu, C. (2015). Convex hulls of random walks and their scaling limits. Stochastic Processes and their Applications, 125(11), 4300-4320. https://doi.org/10.1016/j.spa.2015.06.008

For the perimeter length and the area of the convex hull of the first n steps of a planar random walk, we study n→∞ mean and variance asymptotics and establish non-Gaussian distributional limits. Our results apply to random walks with drift (for the... Read More about Convex hulls of random walks and their scaling limits.

Phase transitions for random geometric preferential attachment graphs (2015)
Journal Article
Jordan, J., & Wade, A. R. (2015). Phase transitions for random geometric preferential attachment graphs. Advances in Applied Probability, 47(2), 565-588. https://doi.org/10.1239/aap/1435236988

Vertices arrive sequentially in space and are joined to existing vertices at random according to a preferential rule combining degree and spatial proximity. We investigate phase transitions in the resulting graph as the relative strengths of these tw... Read More about Phase transitions for random geometric preferential attachment graphs.

Convergence in a multidimensional randomized Keynesian beauty contest (2015)
Journal Article
Grinfeld, M., Volkov, S., & Wade, A. R. (2015). Convergence in a multidimensional randomized Keynesian beauty contest. Advances in Applied Probability, 47(1), 57-82. https://doi.org/10.1239/aap/1427814581

We study the asymptotics of a Markovian system of N ≥ 3 particles in [0, 1]d in which, at each step in discrete time, the particle farthest from the current centre of mass is removed and replaced by an independent U[0, 1]d random particle. We show th... Read More about Convergence in a multidimensional randomized Keynesian beauty contest.