All Outputs (4)

Multivariate normal approximation in geometric probability (2008)
Journal Article
Penrose, M. D., & Wade, A. R. (2008). Multivariate normal approximation in geometric probability. Journal of statistical theory and practice, 2(2), 293-326. https://doi.org/10.1080/15598608.2008.10411876

Consider a measure = Px xx where the sum is over points x of a Poisson point process of intensity on a bounded region in d-space, and x is a functional determined by the Poisson points near to x, i.e. satisfying an exponential stabilization condition... Read More about Multivariate normal approximation in geometric probability.

Limit theory for the random on-line nearest-neighbor graph (2008)
Journal Article
Penrose, M. D., & Wade, A. R. (2008). Limit theory for the random on-line nearest-neighbor graph. Random Structures and Algorithms, 32(2), 125-156. https://doi.org/10.1002/rsa.20185

In the on-line nearest-neighbor graph (ONG), each point after the first in a sequence of points in ℝd is joined by an edge to its nearest neighbor amongst those points that precede it in the sequence. We study the large-sample asymptotic behavior of... Read More about Limit theory for the random on-line nearest-neighbor graph.

Logarithmic speeds for one-dimensional perturbed random walks in random environments (2008)
Journal Article
Menshikov, M., & Wade, A. R. (2008). Logarithmic speeds for one-dimensional perturbed random walks in random environments. Stochastic Processes and their Applications, 118(3), 389-416. https://doi.org/10.1016/j.spa.2007.04.011

We study the random walk in a random environment on Z+={0,1,2,…}, where the environment is subject to a vanishing (random) perturbation. The two particular cases that we consider are: (i) a random walk in a random environment perturbed from Sinai’s r... Read More about Logarithmic speeds for one-dimensional perturbed random walks in random environments.

Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains (2008)
Journal Article
Menshikov, M., Vachkovskaia, M., & Wade, A. (2008). Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains. Journal of Statistical Physics, 132(6), 1097-1133. https://doi.org/10.1007/s10955-008-9578-z

We study stochastic billiards in infinite planar domains with curvilinear boundaries: that is, piecewise deterministic motion with randomness introduced via random reflections at the domain boundary. Physical motivation for the process originates wit... Read More about Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains.