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The Mittag-Leffler process and a scaling limit for the block counting process of the Bolthausen-Sznitman coalescent

- Martin Mohle
- Mathematics
- 27 October 2014

The Mittag–Leffler process X = (Xt)t≥0 is introduced. This Markov process has the property that its marginal random variables Xt are Mittag–Leffler distributed with parameter e, t ∈ [0,∞), and the… Expand

On the number of collisions in beta(2, b)-coalescents

- A. Iksanov, A. Marynych, Martin Mohle
- Mathematics
- 1 August 2009

Expansions are provided for the moments of the number of collisions $X_n$ in the $\beta(2,b)$-coalescent restricted to the set $\{1,...,n\}$. We verify that $X_n/\mathbb{E}X_n$ converges almost… Expand

On the block counting process and the fixation line of the Bolthausen-Sznitman coalescent

- J. Kukla, Martin Mohle
- Mathematics
- 15 April 2016

On a random recursion related to absorption times of death Markov chains

- A. Iksanov, Martin Mohle
- Mathematics
- 31 October 2007

Let $X_1,X_2,...$ be a sequence of random variables satisfying the distributional recursion $X_1=0$ and $X_n= X_{n-I_n}+1$ for $n=2,3,...$, where $I_n$ is a random variable with values in… Expand

On the block counting process and the fixation line of exchangeable coalescents

- F. Gaiser, Martin Mohle
- Mathematics
- 30 March 2016

We study the block counting process and the fixation line of exchangeable coalescents. Formulas for the infinitesimal rates of both processes are provided. It is shown that the block counting process… Expand

Asymptotics of continuous-time discrete state space branching processes for large initial state

- Martin Mohle, Benedict Vetter
- Mathematics
- 14 February 2020

Scaling limits for continuous-time branching processes with discrete state space are provided as the initial state tends to infinity. Depending on the finiteness or non-finiteness of the mean and/or… Expand

Absorption time and tree length of the Kingman coalescent and the Gumbel distribution

- Martin Mohle, Helmut H. Pitters
- Mathematics
- 13 February 2015

Formulas are provided for the cumulants and the moments of the time $T$ back to the most recent common ancestor of the Kingman coalescent. It is shown that both the $j$th cumulant and the $j$th… Expand

On the stationary distribution of the block counting process for population models with mutation and selection

- F. Cordero, Martin Mohle
- MathematicsJournal of Mathematical Analysis and Applications
- 11 May 2018

The collision spectrum of $\Lambda$-coalescents

- A. Gnedin, A. Iksanov, A. Marynych, Martin Mohle
- Physics, MathematicsThe Annals of Applied Probability
- 13 August 2017

$\Lambda$-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… Expand

On the size of the block of 1 for $\varXi$-coalescents with dust

- F. Freund, Martin Mohle
- Mathematics
- 17 March 2017

We study the frequency process $f_1$ of the block of 1 for a $\varXi$-coalescent $\varPi$ with dust. If $\varPi$ stays infinite, $f_1$ is a jump-hold process which can be expressed as a sum of broken… Expand

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