Related papers: Second-order asymptotics for the block counting pr…

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 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…

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…

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…

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…

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…

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…

In this work, we approach the problem of finding the zeros of a continuous and monotone operator through a second-order dynamical system with a damping term of the form $1/t^{r}$, where $r\in [0, 1]$. The system features the time derivative…

$\Lambda$-coalescents model the evolution of a coalescing system in which any number of blocks randomly sampled from the whole may merge into a larger block. For the coalescent restricted to initially $n$ singletons we study the collision…

We show that the total number of collisions in the exchangeable coalescent process driven by the beta $(1,b)$ measure converges in distribution to a 1-stable law, as the initial number of particles goes to infinity. The stable limit law is…

We study some aspects of the absorption time of the Beta$(a,b)$-Coalescent starting with $n$ blocks. More precisely, when $a>1$, the absorption time is known to converge to infinity as $n$ goes to infinity, and we prove that it satisfies a…

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…

In this work, we study general Dirichlet coalescents, which are a family of Xi-coalecents constructed from i.i.d mass partitions, and are an extension of the symmetric coalescent. This class of models is motivated by population models with…

In the asymptotic theory of quantum hypothesis testing, the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states…

In this paper, we consider Beta$(2-{\alpha},{\alpha})$ (with $1<{\alpha}<2$) and related ${\Lambda}$-coalescents. If $T^{(n)}$ denotes the length of an external branch of the $n$-coalescent, we prove the convergence of…

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 $\X$-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…

Consider a branching system with particles moving according to an Ornstein-Uhlenbeck process with drift $\mu>0$ and branching according to a law in the domain of attraction of the $(1+\beta)$-stable distribution. The mean of the branching…

If a partition $\lambda$ of size n is chosen randomly according to the Plancherel measure $P_n[\lambda] = (\dim \lambda)^2/n!$, then as n goes to infinity, the rescaled shape of $\lambda$ is with high probability very close to a non-random…

In this paper we look at the asymptotic number of r-caterpillars for $\Lambda$-coalescents which come down from infinity, under a regularly varying assumption. An r-caterpillar is a functional of the coalescent process started from $n$…