13 citations · 37 across the 6 of their papers we have counts for
6 papers
Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips
Ostap Hryniv, Iain M. MacPhee, Mikhail V. Menshikov +1
We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non-existence o…
Dynamics of the supermarket model
I. M. MacPhee, M. V. Menshikov, M. Vachkovskaia
We consider the long term behaviour of a Markov chain ξ(t) on \Z^N based on the N station supermarket model. Different routing policies for the supermarket model give different Mar…
Angular asymptotics for multi-dimensional non-homogeneous random walks with asymptotically zero drift
Iain M. MacPhee, Mikhail V. Menshikov, Andrew R. Wade
We study the first exit time from an arbitrary cone with apex at the origin by a non-homogeneous random walk (Markov chain) on () with mean drift that is asymp…
Passage-time moments and hybrid zones for the exclusion-voter model
Iain M. MacPhee, Mikhail V. Menshikov, Stanislav Volkov +1
We study the non-equilibrium dynamics of a one-dimensional interacting particle system that is a mixture of the voter model and the exclusion process. With the process started from…
Moments of exit times from wedges for non-homogeneous random walks with asymptotically zero drifts
Iain M. MacPhee, Mikhail V. Menshikov, Andrew R. Wade
We study quantitative asymptotics of planar random walks that are spatially non-homogeneous but whose mean drifts have some regularity. Specifically, we study the first exit time $…
Periodicity in the transient regime of exhaustive polling systems
I. M. MacPhee, M. V. Menshikov, S. Popov +1
We consider an exhaustive polling system with three nodes in its transient regime under a switching rule of generalized greedy type. We show that, for the system with Poisson arriv…