Related papers: Kingman's coalescent with erosion

Kingman Coalescent was first proposed by Kingman [7] in population genetics to describe population's genealogical structure. Now it becomes a bench-mark model for coalescent process. Extensive studies have been conducted on Kingman…

We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…

Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…

For a one-locus haploid infinite population with discrete generations, the celebrated Kingman's model describes the evolution of fitness distributions under the competition of selection and mutation, with a constant mutation probability.…

We consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long…

A novel strategy that combines a given collection of $\pi$-reversible Markov kernels is proposed. At each Markov transition, one of the available kernels is selected via a state-dependent probability distribution. In contrast to random-scan…

Similarly as in (Blancas et al. 2018) where nested coalescent processes are studied, we generalize the definition of partition-valued homogeneous Markov fragmentation processes to the setting of nested partitions, i.e. pairs of partitions…

We introduce a new Wright-Fisher type model for seed banks incorporating "simultaneous switching", which is motivated by recent work on microbial dormancy. We show that the simultaneous switching mechanism leads to a new jump-diffusion…

In this paper we extend two limit theorems which were recently obtained for fragmentation processes to such processes with immigration. More precisely, in the setting with immigration we consider a limit theorem for the process counted with…

We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving…

We consider randomized dynamics over the $n$-simplex, where at each step a random set, or block, of coordinates is evenly averaged. When all blocks have size 2, this reduces to the repeated averages studied in [CDSZ22], a version of the…

This paper generalizes the strong seed-bank model introduced in arXiv:1411.4747 to allow for more general dormancy time distributions, such as a type of Pareto distribution. Inspired by the method of approximation using models with…

Motivated by kinetically constrained interacting particle systems (KCM), we consider a reversible coalescing and branching simple exclusion process on a general finite graph $G=(V,E)$ dual to the biased voter model on $G$. Our main goal are…

Assume that individuals alive at time $t$ in some population can be ranked in such a way that the coalescence times between consecutive individuals are i.i.d. The ranked sequence of these branches is called a coalescent point process. We…

Plant differently colored points in the plane, then let random points ("Poisson rain") fall, and give each new point the color of the nearest existing point. Previous investigation and simulations strongly suggest that the colored regions…

We consider a non-conserving zero-range process with hopping rate proportional to the number of particles at each site. Particles are added to the system with a site-dependent creation rate, and removed from the system with a uniform…

The paper discusses the continuous-time Markov Branching Process allowing Immigration. We are considering a critical case for which the second moment of offspring law and the first moment of immigration law are possibly infinite. Assuming…

Let $K_n$ denote the number of types of a sample of size $n$ taken from an exchangeable coalescent process ($\Xi$-coalescent) with mutation. A distributional recursion for the sequence $(K_n)_{n\in{\mathbb N}}$ is derived. If the coalescent…

Inertial particles suspended in many natural and industrial flows undergo coagulation upon collisions and fragmentation if their size becomes too large or if they experience large shear. Here we study this coagulation-fragmentation process…

Analogues of stepping--stone models are considered where the site--space is continuous, the migration process is a general Markov process, and the type--space is infinite. Such processes were defined in previous work of the second author by…