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We study a two dimensional version of Neuhauser’s long range sexual reproduction model and prove results that give bounds on the critical values λ f for that the process to survive from a finite set and λe for the existence of a nontrivial stationary distribution. Our first result comes from a standard block construction, while the second involves a… (More)

- Mariya Bessonov, Alexey Ovchinnikov, Maxwell Shapiro
- ISSAC
- 2013

We study integrability conditions for systems of parameterized linear difference equations and related properties of linear differential algebraic groups. We show that isomonodromicity of such a system is equivalent to isomonodromicity with respect to each parameter separately under a linearly differentially closed assumption on the field of differential… (More)

We approximate the Bolker-Pacala model of population dynamics with the logistic Markov chain and analyze the latter. We find the asymptotics of the degenerated hypergeometric function and use these to prove a local CLT and large deviations result. We also state global limit theorems and obtain asymptotics for the first passage time to the boundary of a… (More)

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