相关论文: Two-sided immigration, emigration and symmetry pro…
We prove a long-standing conjecture which characterises the Ewens-Pitman two-parameter family of exchangeable random partitions, plus a short list of limit and exceptional cases, by the following property: for each $n = 2,3, >...$, if one…
The recently introduced two-parameter Poisson-Dirichlet diffusion extends the infinitely-many-neutral-alleles model, related to Kingman's distribution and to Fleming-Viot processes. The role of the additional parameter has been shown to…
Under a fourth order moment condition on the branching and a second order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous state and continuous…
Populations exhibiting partial migration consist of two groups of individuals: Those that mi- grate between habitats, and those that remain fixed in a single habitat. We propose several discrete-time population models to investigate the…
The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that…
A superprocess with dependent spatial motion and interactive immigration is constructed as the pathwise unique solution of a stochastic integral equation carried by a stochastic flow and driven by Poisson processes of one-dimensional…
In distributed evolutionary algorithms, migration interval is used to decide migration moments. Nevertheless, migration moments predetermined by intervals cannot match the dynamic situation of evolution. In this paper, a scheme of setting…
An Allee effect occurs when the per-capita growth rate increases at low densities. Here, we investigate the evolutionary stability of a partial migration population with migrant population experiencing Allee effects. Partial migration is a…
Host-parasitoid population dynamics is often probed using a semi-discrete/hybrid modeling framework. Here, the update functions in the discrete-time model connecting year-to-year changes in the population densities are obtained by solving…
We consider the interacting Bessel processes, a family of multiple-particle systems in one dimension where particles evolve as individual Bessel processes and repel each other via a log-potential. We consider two limiting regimes for this…
Motivated by tumor growth and spatial population genetics, we study the interplay between evolutionary and spatial dynamics at the surfaces of three-dimensional, spherical range expansions. We consider range expansion radii that grow with…
The two parameter Poisson-Dirichlet Process (PDP), a generalisation of the Dirichlet Process, is increasingly being used for probabilistic modelling in discrete areas such as language technology, bioinformatics, and image analysis. There is…
The aim of the paper is to introduce a two-parameter family of infinite-dimensional diffusion processes X(alpha,theta) related to Pitman's two-parameter Poisson-Dirichlet distributions PD(alpha,theta). The diffusions X(alpha,theta) are…
We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…
The Poisson--Dirichlet distribution arises in many different areas. The parameter $\theta$ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting case of $\theta$ approaching…
In this article we focus on the partial sum $S_{n}=X_{1}+\cdots+X_{n}$ of the subcritical branching process with immigration $\{X_{n}\}_{n\in\mathbb{N_{+}}}$, under the condition that one of the offspring $\xi$ or immigration $\eta$ is…
In this paper we give a new example of duality between fragmentation and coagulation operators. Consider the space of partitions of mass (i.e., decreasing sequences of nonnegative real numbers whose sum is 1) and the two-parameter family of…
The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that…
The partition function $p(n)$, which counts the number of partitions of a positive integer $n$, is widely studied. Here, we study partition functions $p_S(n)$ that count partitions of $n$ into distinct parts satisfying certain congruence…
We introduce diffusions on a space of interval partitions of the unit interval that are stationary with the Poisson-Dirichlet laws with parameters $(\alpha,0)$ and $(\alpha,\alpha)$. The construction has two steps. The first is a general…