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6 papers · 2 filters
Gaussian limits for multidimensional random sequential packing at saturation (extended version)
T. Schreiber, Mathew D. Penrose, J. E. Yukich
Consider the random sequential packing model with infinite input and in any dimension. When the input consists of non-zero volume convex solids we show that the total number of sol…
Classes of Skorokhod Embeddings for the Simple Symmetric Random Walk
Alexander M. G. Cox, Jan Obloj
The Skorokhod Embedding problem is well understood when the underlying process is a Brownian motion. We examine the problem when the underlying is the simple symmetric random walk…
Random walk in random environment with asymptotically zero perturbation
M. V. Menshikov, Andrew R. Wade
We give criteria for ergodicity, transience and null recurrence for the random walk in random environment on {0,1,2,...}, with reflection at the origin, where the random environmen…
Growth and roughness of the interface for ballistic deposition
Mathew D. Penrose
In ballistic deposition (BD), -dimensional particles fall sequentially at random towards an initially flat, large but bounded -dimensional surface, and each particle stic…
Weak and almost sure limits for the parabolic Anderson model with heavy tailed potentials
Remco van der Hofstad, Peter Mörters, Nadia Sidorova\tsup
We study the parabolic Anderson problem, that is, the heat equation on with independent identically distributed random potentia…
Limit theory for the random on-line nearest-neighbour graph
Mathew D. Penrose, Andrew R. Wade
In the on-line nearest-neighbour graph (ONG), each point after the first in a sequence of points in R^d is joined by an edge to its nearest-neighbour amongst those points that prec…