Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Forman, Noah"'
Motivated by a down-up Markov chain on cladograms, David Aldous conjectured in 1999 that there exists a "diffusion on continuum trees" whose mass partitions at any finite number of branch points evolve as Wright-Fisher diffusions with some negative m
Externí odkaz:
http://arxiv.org/abs/2305.17269
In previous work, we constructed Fleming--Viot-type measure-valued diffusions (and diffusions on a space of interval partitions of the unit interval $[0,1]$) that are stationary with the Poisson--Dirichlet laws with parameters $\alpha\in(0,1)$ and $\
Externí odkaz:
http://arxiv.org/abs/2101.09307
We introduce and study interval partition diffusions with Poisson--Dirichlet$(\alpha,\theta)$ stationary distribution for parameters $\alpha\in(0,1)$ and $\theta\ge 0$. This extends previous work on the cases $(\alpha,0)$ and $(\alpha,\alpha)$ and bu
Externí odkaz:
http://arxiv.org/abs/2008.02823
Publikováno v:
Ann. Appl. Probab. 32 (3) 2211 - 2253, 2022
We give a pathwise construction of a two-parameter family of purely-atomic-measure-valued diffusions in which ranked masses of atoms are stationary with the Poisson-Dirichlet$(\alpha,\theta)$ distributions, for $\alpha\in (0,1)$ and $\theta\ge 0$. Th
Externí odkaz:
http://arxiv.org/abs/2007.05250
We introduce diffusions on a space of interval partitions of the unit interval that are stationary with the Poisson-Dirichlet laws with parameters $(\alpha,0)$ and $(\alpha,\alpha)$. The construction has two steps. The first is a general construction
Externí odkaz:
http://arxiv.org/abs/1910.07626
Consider a spectrally positive Stable($1+\alpha$) process whose jumps we interpret as lifetimes of individuals. We mark the jumps by continuous excursions assigning "sizes" varying during the lifetime. As for Crump-Mode-Jagers processes (with "charac
Externí odkaz:
http://arxiv.org/abs/1909.02584
Publikováno v:
Electron. Commun. Probab., Volume 25 (2020), paper no. 38, 16 pp
We first consider interval partitions whose complements are Lebesgue-null and introduce a complete metric that induces the same topology as the Hausdorff distance (between complements). This is done using correspondences between intervals. Further re
Externí odkaz:
http://arxiv.org/abs/1907.02132
The Aldous diffusion is a conjectured Markov process on the space of real trees that is the continuum analogue of discrete Markov chains on binary trees. We construct this conjectured process via a consistent system of stationary evolutions of binary
Externí odkaz:
http://arxiv.org/abs/1809.07756
We construct a stationary Markov process corresponding to the evolution of masses and distances of subtrees along the spine from the root to a branch point in a conjectured stationary, continuum random tree-valued diffusion that was proposed by David
Externí odkaz:
http://arxiv.org/abs/1804.01205
Consider the Aldous Markov chain on the space of rooted binary trees with $n$ labeled leaves in which at each transition a uniform random leaf is deleted and reattached to a uniform random edge. Now, fix $1\le k < n$ and project the leaf mass onto th
Externí odkaz:
http://arxiv.org/abs/1802.00862