Zobrazeno 1 - 10
of 37
pro vyhledávání: '"Stephenson, Robin"'
Autor:
Haas, Bénédicte, Stephenson, Robin
We introduce multi-type Markov Branching trees, which are simple random population tree models where individuals are characterized by their size and type and give rise to (size,type)-children in a Galton-Watson fashion, with the rule that the size of
Externí odkaz:
http://arxiv.org/abs/1912.07296
We consider the random directed graph $\vec{G}(n,p)$ with vertex set $\{1,2,\ldots,n\}$ in which each of the $n(n-1)$ possible directed edges is present independently with probability $p$. We are interested in the strongly connected components of thi
Externí odkaz:
http://arxiv.org/abs/1905.05397
Autor:
Stephenson, Robin
A Markov Additive Process is a bi-variate Markov process $(\xi,J)=\big((\xi_t,J_t),t\geq0\big)$ which should be thought of as a multi-type L\'evy process: the second component $J$ is a Markov chain on a finite space $\{1,\ldots,K\}$, and the first co
Externí odkaz:
http://arxiv.org/abs/1706.03495
Autor:
Stephenson, Robin
Nous nous intéressons à trois problèmes issus du monde des arbres aléatoires discrets et continus. Dans un premier lieu, nous faisons une étude générale des arbres de fragmentation auto-similaires, étendant certains résultats de Haas et Mier
Externí odkaz:
http://www.theses.fr/2014PA090024/document
Autor:
Haas, Bénédicte, Stephenson, Robin
Motivated by various applications, we describe the scaling limits of bivariate Markov chains $(X,J)$ on $\mathbb Z_+ \times \{1,\ldots,\kappa\}$ where $X$ can be viewed as a position marginal and $\{1,\ldots,\kappa\}$ is a set of $\kappa$ types. The
Externí odkaz:
http://arxiv.org/abs/1612.06058
Autor:
Bertoin, Jean, Stephenson, Robin
Markovian growth-fragmentation processes describe a family of particles which can grow larger or smaller with time, and occasionally split in a conservative manner. They were introduced in a work of Bertoin, where special attention was given to the s
Externí odkaz:
http://arxiv.org/abs/1602.04957
Autor:
Stephenson, Robin
We show that large critical multi-type Galton-Watson trees, when conditioned to be large, converge locally in distribution to an infinite tree which is analoguous to Kesten's infinite monotype Galton-Watson tree. This is proven when we condition on t
Externí odkaz:
http://arxiv.org/abs/1412.6911
Autor:
Haas, Bénédicte, Stephenson, Robin
For each integer $k \geq 2$, we introduce a sequence of $k$-ary discrete trees constructed recursively by choosing at each step an edge uniformly among the present edges and grafting on "its middle" $k-1$ new edges. When $k=2$, this corresponds to a
Externí odkaz:
http://arxiv.org/abs/1402.1084
Autor:
Stephenson, Robin
We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured real tree. Under some Malthusian hypotheses, we compute the fractal Hausdorff dimension of this tree through the use of a natural measure on the
Externí odkaz:
http://arxiv.org/abs/1303.6873