Nicholas Georgiou

activity

20172020

collaborators

4 papers

math.PR2020

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…

math.PR2018

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 $R_{+}$ , $R$ , and $R^{2}$ whose increments have heavy tails with exponent in $(1, 2)$ …

math.PR2018

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 $R^{d}$ , which may be recurrent in any dimension. The limit $\mathcal{X}…

math.PR2017

A radial invariance principle for non-homogeneous random walks

Nicholas Georgiou, Aleksandar Mijatović, Andrew R. Wade

Consider non-homogeneous zero-drift random walks in $R^{d}$ , $d \geq 2$ , with the asymptotic increment covariance matrix $σ^{2} (u)$ satisfying $\mathbf{u}^\top σ^2 (…