Thomas Duquesne, Jean-Francois Le Gall
We prove a strong form of the invariance under re-rooting of the distribution of the continuous random trees called Levy trees. This extends previous results due to several authors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson--Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coarse one by shattering each of its parts independently, according to the same law. As a second application of spinal decompositions, we prove that among the continuous fragmentation trees, stable trees a…
We study the diameter of L{é}vy trees that are random compact metric spaces obtained as the scaling limits of Galton-Watson trees. L{é}vy trees have been introduced by Le Gall and Le Jan (1998) and they generalise Aldous' Continuum Random Tree (1991) that corresponds to the Brownian case. We first characterize the law of the diameter of L{é}vy trees and we prove that it is realized by a unique pair of points. We prove that the law of L{é}vy trees conditioned to have a fixed diameter r $\in$ (0, $\infty$) is obtained by glueing at their respective roots two independent size-biased L{é}vy trees …
In this note we prove the well-posedness for stochastic 2D Navier-Stokes equation driven by general Lévy processes (in particular, $α$-stable processes), and obtain the existence of invariant measures.
We study such important properties of $f$-divergence minimal martingale measure as Levy preservation property, scaling property, invariance in time property for exponential Levy models. We give some useful decomposition for $f$-divergence minimal martingale measures and we answer on the question which form should have $f$ to ensure mentioned properties. We show that $f$ is not necessarily common $f$-divergence. For common $f$-divergences, i.e. functions verifying $f"(x) = ax^ γ,\, a>0,\, γ\in \mathbb R$, we give necessary and sufficient conditions for existence of $f$-minimal martingale measur…
The $\mathcal{A}$-tracial algebras are algebras endowed with multi-linear forms, compatible with the product, and indexed by partitions. Using the notion of $\mathcal{A}$-cumulants, we define and study the $\mathcal{A}$-freeness property which generalizes the independence and freeness properties, and some invariance properties which model the invariance by conjugation for random matrices. A central limit theorem is given in the setting of $\mathcal{A}$-tracial algebras. A generalization of the normalized moments for random matrices is used to define convergence in $\mathcal{A}$-distribution: t…
Pruning processes $(\mathcal{F}(θ),θ\geq 0)$ have been studied separately for Galton-Watson trees and for Lévy trees/forests. We establish here a limit theory that strongly connects the two studies. This solves an open problem by Abraham and Delmas, also formulated as a conjecture by Löhr, Voisin and Winter. Specifically, we show that for any sequence of Galton-Watson forests $\mathcal{F}_n$, $n\geq 1$, in the domain of attraction of a Lévy forest $\mathcal{F}$, suitably scaled pruning processes $(\mathcal{F}_n(θ),θ\geq 0)$ converge in the Skorohod topology on cadlag functions with values in t…
We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional Lévy processes. The technique used is interesting in itself; it extends an older idea of splitting a sample into a central part and an extreme one, analyzing each part with different techniques, and then combining the results. This technique seems to have the potential to be useful in other problems in the domain of nonGaussian stable distributions.
We introduce the notion of a hereditary property for rooted real trees and we also consider reduction of trees by a given hereditary property. Leaf-length erasure, also called trimming, is included as a special case of hereditary reduction. We only consider the metric structure of trees, and our framework is the space $\bT$ of pointed isometry classes of locally compact rooted real trees equipped with the Gromov-Hausdorff distance. Some of the main results of the paper are a general tightness criterion in $\bT$ and limit theorems for growing families of trees. We apply these results to Galton-…
We investigate the genealogical structure of general critical or subcritical continuous-state branching processes. Analogously to the coding of a discrete tree by its contour function, this genealogical structure is coded by a real-valued stochastic process called the height process, which is itself constructed as a local time functional of a Levy process with no negative jumps. We present a detailed study of the height process and of an associated measure-valued process called the exploration process, which plays a key role in most applications. Under suitable assumptions, we prove that whene…
Invariance principle for fragmentation processes derived from conditioned stable Galton-Watson trees
本文研究条件临界稳定 Galton–Watson 树随机删边所得碎裂过程，证明其重标度后收敛到 $\alpha$-稳定 Lévy 树的比例切割碎裂，并通过稳定 Lévy 游程划分给出构造，推广 Brownian CRT 结果。
We are interested in the asymptotic behavior of critical Galton-Watson trees whose offspring distribution may have infinite variance, which are conditioned on having a large fixed number of leaves. We first find an asymptotic estimate for the probability of a Galton-Watson tree having $n$ leaves. Secondly, we let $t_n$ be a critical Galton-Watson tree whose offspring distribution is in the domain of attraction of a stable law, and conditioned on having exactly $n$ leaves. We show that the rescaled Lukasiewicz path and contour function of $t_n$ converge respectively to $X^{exc}$ and $H^{exc}$, …
The subject of this paper is the study of convolution semigroups of states on a locally compact quantum group, generalising classical families of distributions of a Lévy process on a locally compact group. In particular a definitive one-to-one correspondence between symmetric convolution semigroups of states and noncommutative Dirichlet forms satisfying the natural translation invariance property is established, extending earlier partial results and providing a powerful tool to analyse such semigroups. This is then applied to provide new characterisations of the Haagerup Property and Property …
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。