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## Random Recursive Trees and the Bolthausen-Sznitman Coalesent

- C. Goldschmidt, James B. Martin
- Mathematics
- 13 February 2005

We describe a representation of the Bolthausen-Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the… Expand

## The continuum limit of critical random graphs

- L. Addario-Berry, N. Broutin, C. Goldschmidt
- Mathematics
- 27 March 2009

We consider the Erdős–Rényi random graph G(n, p) inside the critical window, that is when p = 1/n + λn−4/3, for some fixed $${\lambda \in \mathbb{R}}$$ . We prove that the sequence of connected… Expand

## A line-breaking construction of the stable trees

- C. Goldschmidt, Bénédicte Haas
- Mathematics
- 21 July 2014

We give a new, simple construction of the $\alpha$-stable tree for $\alpha \in (1,2]$. We obtain it as the closure of an increasing sequence of $\mathbb{R}$-trees inductively built by gluing together… Expand

## Coagulation-fragmentation duality, Poisson-Dirichlet distributions and random recursive trees

- R. Dong, C. Goldschmidt, James B. Martin
- Mathematics
- 28 July 2005

In this paper we give a new example of duality between fragmentation and coagulation operators. Consider the space of partitions of mass (i.e., decreasing sequences of nonnegative real numbers whose… Expand

## Dual Random Fragmentation and Coagulation and an Application to the Genealogy of Yule Processes

- J. Bertoin, C. Goldschmidt
- Mathematics
- 10 August 2004

The purpose of this work is to describe a duality betweena fragmentationassociated to certain Dirichlet distributions and a natural randomcoagulation. The dualfragmentation and coalescent chains… Expand

## The stable graph: the metric space scaling limit of a critical random graph with i.i.d. power-law degrees

- Guillaume Conchon--Kerjan, C. Goldschmidt
- Mathematics, Computer Science
- 12 February 2020

We prove a metric space scaling limit for a critical random graph with independent and identically distributed degrees having power-law tail behaviour with exponent $\alpha+1$, where $\alpha \in… Expand

## The Brownian continuum random tree as the unique solution to a fixed point equation

- M. Albenque, C. Goldschmidt
- Mathematics
- 21 April 2015

© 2015, University of Washington. All rights reserved. In this note, we provide a new characterization of Aldous’ Brownian continuum random tree as the unique fixed point of a certain natural… Expand

## Behavior near the extinction time in self-similar fragmentations I: The stable case

- C. Goldschmidt, Bénédicte Haas
- Mathematics
- 7 May 2008

The stable fragmentation with index of self-similarity $\alpha \in [-1/2,0)$ is derived by looking at the masses of the subtrees formed by discarding the parts of a $(1 + \alpha)^{-1}$--stable… Expand

## Asymptotics of the allele frequency spectrum associated with the Bolthausen-Sznitman coalescent

- Anne-Laure Basdevant, C. Goldschmidt
- Mathematics
- 19 June 2007

## Quantum Heisenberg models and their probabilistic representations

- C. Goldschmidt, D. Ueltschi, P. Windridge
- Mathematics
- 6 April 2011

These notes give a mathematical introduction to two seemingly unrelated topics: (i) quantum spin systems and their cycle and loop representa- tions, due to T oth and Aizenman-Nachtergaele; (ii)… Expand

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