8 citations · 31 across the 8 of their papers we have counts for
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Gaussian and non-Gaussian limits for the total edge-length of random directional nearest-neighbour graphs
Nicholas Georgiou, Qasem M. Tawhari, Andrew Wade
We study planar random spatial graphs defined by inserting an edge between every point of a homogeneous Poisson process on the unit square and a nearest-neighbour within a fixed co…
Deposition, diffusion, and nucleation on an interval
Nicholas Georgiou, Andrew R. Wade
Motivated by nanoscale growth of ultra-thin films, we study a model of deposition, on an interval substrate, of particles that perform Brownian motions until any two meet, when the…
Markov chains with heavy-tailed increments and asymptotically zero drift
Nicholas Georgiou, Mikhail V. Menshikov, Dimitri Petritis +1
We study the recurrence/transience phase transition for Markov chains on , , and whose increments have heavy tails with exponent in …
Invariance principle for non-homogeneous random walks
Nicholas Georgiou, Aleksandar Mijatović, Andrew R. Wade
We prove an invariance principle for a class of zero-drift spatially non-homogeneous random walks in , which may be recurrent in any dimension. The limit $\mathcal{X}…
A radial invariance principle for non-homogeneous random walks
Nicholas Georgiou, Aleksandar Mijatović, Andrew R. Wade
Consider non-homogeneous zero-drift random walks in , , with the asymptotic increment covariance matrix satisfying $\mathbf{u}^\top σ^2 (…
Anomalous recurrence properties of many-dimensional zero-drift random walks
Nicholas Georgiou, Mikhail V. Menshikov, Aleksandar Mijatović +1
Famously, a -dimensional, spatially homogeneous random walk whose increments are non-degenerate, have finite second moments, and have zero mean is recurrent if b…
Non-homogeneous random walks on a semi-infinite strip
Nicholas Georgiou, Andrew R. Wade
We study the asymptotic behaviour of Markov chains on , where is the non-negative integers and is a finite set. Neither coordi…
The simple harmonic urn
Edward Crane, Nicholas Georgiou, Stanislav Volkov +2
We study a generalized Pólya urn model with two types of ball. If the drawn ball is red, it is replaced together with a black ball, but if the drawn ball is black it is replaced an…