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Branching Brownian motion seen from its tip
It has been conjectured since the work of Lalley and Sellke (Ann. Probab., 15, 1052–1061, 1987) that branching Brownian motion seen from its tip (e.g. from its rightmost particle) converges to an…
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Exchangeable Fragmentation-Coalescence Processes and their Equilibrium Measures
We define and study a family of Markov processes with state space the compact set of all partitions of $N$ that we call exchangeable fragmentation-coalescence processes. They can be viewed as a…
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Small-time behavior of beta coalescents
For a finite measureon (0,1), the �-coalescent is a coalescent process such that, whenever there are b clusters, each k-tuple of clusters merges into one at rate R 1 0 x k 2 (1 x) b k �(dx). It has…
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BETA-COALESCENTS AND CONTINUOUS STABLE RANDOM TREES
TLDR
It is proved that Beta-coalescents can be embedded in continuous stable random trees based on a construction of the Donnelly-Kurtz lookdown process using continuous random trees, which is of independent interest.
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Ranked Fragmentations
. In this paper we define and study self-similar ranked fragmentations. We first show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a…
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The genealogy of branching Brownian motion with absorption
We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly…
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The Λ-coalescent speed of coming down from infinity
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…
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The number of accessible paths in the hypercube
TLDR
If the value on $(0,0,\ldots,0)$ is set to $x=X/L $ then $\Theta/L$ converges in law as $L\to\infty$ to $\mathrm{e}^{-X}$ times the product of two standard independent exponential variables.
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Multifractal Spectra of Fragmentation Processes
AbstractLet (S(t),t≥0) be a homogeneous fragmentation of ]0,1[ with no loss of mass. For x∈]0,1[, we say that the fragmentation speed of x is v if and only if, as time passes, the size of the…
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The prolific backbone for supercritical superdiffusions
We develop an idea of Evans and O'Connell, Englander and Pinsky and Duquesne and Winkel by giving a pathwise construction of the so called `backbone' decomposition for supercritical superprocesses.…
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