Related papers: Scaling Limits of Coalescent Processes Near Time Z…

We provide scaling limits for the block counting process and the fixation line of $\Lambda$-coalescents as the initial state $n$ tends to infinity under the assumption that the measure $\Lambda$ on $[0,1]$ satisfies…

An important property of Kingman's coalescent is that, starting from a state with an infinite number of blocks, over any positive time horizon, it transitions into an almost surely finite number of blocks. This is known as `coming down from…

We consider standard $\La$-coalescents (or coalescents with multiple collisions) with a non-trivial "Kingman part". Equivalently, the driving measure $\Lambda$ has an atom at $0$; $\Lambda(\{0\})=c>0$. It is known that all such coalescents…

We describe a simple construction of Kingman's coalescent in terms of a Brownian excursion. This construction is closely related to, and sheds some new light on, earlier work by Aldous and Warren. Our approach also yields some new results:…

A superprocess with coalescing spatial motion is constructed in terms of one-dimensional excursions. Based on this construction, it is proved that the superprocess is purely atomic and arises as scaling limit of a special form of the…

We examine the total number of collisions $C_n$ in the $\Lambda$-coalescent process which starts with $n$ particles. A linear growth and a stable limit law for $C_n$ are shown under the assumption of a power-like behaviour of the measure…

For a finite measure $\varLambda$ on $[0,1]$, the $\varLambda$-coalescent is a coalescent process such that, whenever there are $b$ clusters, each $k$-tuple of clusters merges into one at rate…

For a class of $\Lambda$-Fleming-Viot processes with Brownian spatial motion in $\mathbb{R}^d$ whose associated $\Lambda$-coalescents come down from infinity, we obtain sharp global and local modulus of continuities for the ancestry…

We study several fundamental properties of a class of stochastic processes called spatial Lambda-coalescents. In these models, a number of particles perform independent random walks on some underlying graph G. In addition, particles on the…

Consider a $\Lambda$-coalescent that comes down from infinity (meaning that it starts from a configuration containing infinitely many blocks at time 0, yet it has a finite number $N_t$ of blocks at any positive time $t>0$). We exhibit a…

We consider the lambda-coalescent processes with positive frequency of singleton clusters. The class in focus covers, for instance, the beta$(a,b)$-coalescents with $a>1$. We show that some large-sample properties of these processes can be…

The block counting process with initial state $n$ counts the number of blocks of an exchangeable coalescent ($\Xi$-coalescent) restricted to a sample of size $n$. This work provides scaling limits for the block counting process of regular…

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…

The $\X$-coalescent processes were initially studied by M\"ohle and Sagitov (2001), and introduced by Schweinsberg (2000) in their full generality. They arise in the mathematical population genetics as the complete class of scaling limits…

We prove several limit theorems that relate coalescent processes to continuous-state branching processes. Some of these theorems are stated in terms of the so-called generalized Fleming-Viot processes, which describe the evolution of a…

The $\Lambda$-Fleming-Viot process is a probability measure-valued process that is dual to a $\Lambda$-coalescent that allows multiple collisions. In this paper, we consider a class of $\Lambda$-Fleming-Viot processes with Brownian spatial…

We present a law of large numbers and a central limit theorem for the time to absorption of $\Lambda$-coalescents, started from $n$ blocks, as $n \to \infty$. The proofs rely on an approximation of the logarithm of the block-counting…

This article shows the asymptotics of distributions of various functionals of the Beta$(2-\alpha,\alpha)$ $n$-coalescent process with $1<\alpha<2$ when $n$ goes to infinity. This process is a Markov process taking {values} in the set of…

We revisit the spatial ${\lambda}$-Fleming-Viot process introduced in [1]. Particularly, we are interested in the time $T_0$ to the most recent common ancestor for two lineages. We distinguish between the case where the process acts on the…

Consider a standard ${\Lambda }$-coalescent that comes down from infinity. Such a coalescent starts from a configuration consisting of infinitely many blocks at time $0$, but its number of blocks $N_t$ is a finite random variable at each…