My papers may almost all be found on arXiv or on MathSciNet (subscribers only).

- Essential edges in Poisson random
hypergraphs, with James Norris,
*Random Structures and Algorithms***24**, 4 (2004) pp.381-396. - Dual random fragmentation and
coagulation
and an application to the genealogy of Yule processes,
with Jean
Bertoin, in
*Mathematics and Computer Science III:**Algorithms, Trees, Combinatorics and Probabilities*, M. Drmota, P. Flajolet, D. Gardy, B. Gittenberger (Eds.) (2004) pp.295-308. - Critical random hypergraphs: the
emergence
of a giant set of identifiable vertices,
*Annals of Probability***33**, 4 (2005) pp.1573-1600. - Random recursive trees and the
Bolthausen-Sznitman coalescent, with James Martin,
*Electronic Journal of Probability*,**10**(2005), Paper no. 21, pp.718-745. [Oberwolfach report]. - Preservation of log-concavity on
summation, with Oliver Johnson,
*ESAIM: Probability and Statistics***10**(2006) pp.206-215. - Coagulation-fragmentation duality, Poisson-Dirichlet
distributions and random recursive trees, with Rui Dong and James
Martin,
*Annals of Applied Probability*,**16**, 4 (2006) pp.1733-1750. - Asymptotics of the allele frequency
spectrum associated with the Bolthausen-Sznitman
coalescent, with Anne-Laure Basdevant,
*Electronic Journal of Probability***13**(2008), Paper no. 17, pp.486-512. [Oberwolfach report] - Fragmenting random permutations,
with James Martin and Dario Spanò,
*Electronic Communications in Probability***13**(2008), Paper no. 44, pp.461-474. - Behavior near the extinction time in
self-similar fragmentations I: The stable case, with
Bénédicte Haas,
*Annales de l'Institut Henri Poincaré (Probabilités et Statistiques)***46**, 2 (2010), pp.338-368. (AIHP prized paper) - Critical random graphs: limiting
constructions and distributional properties, with
Louigi Addario-Berry and Nicolas Broutin,
*Electronic Journal of Probability***15**(2010), Paper no. 25, pp.741-775. - Quantum Heisenberg models and their probabilistic representations, with Daniel Ueltschi and Peter Windridge, Entropy and the Quantum II,
*Contemporary Mathematics***552**(2011), pp.177-224. - The continuum limit of critical
random graphs, with Louigi Addario-Berry and
Nicolas
Broutin,
*Probability Theory and Related Fields***152**, 3-4 (2012), pp.367-406.

[Errata: (1) The proof of Lemma 13 given contains an error; see the proof of Theorem 1.1 of Addario-Berry, Devroye and Janson, Sub-Gaussian tail bounds for the width and height of conditioned Galton–Watson trees,*Ann. Probab.***41**, 2 (2013), pp.1072-1087 for a fix. (2) In the proof of Theorem 24 we invoke Brownian scaling in order to get a bound of the height of a tilted tree in terms of its size. This argument is invalid (Brownian scaling does not work for tilted excursions), but may be straightforwardly fixed using the measure change, the Cauchy-Schwarz inequality and the fact that the length of the longest excursion is a.s. finite.] - A line-breaking construction of the
stable trees, with Bénédicte Haas,
*Electronic Journal of Probability***20**(2015), Paper no. 16, pp.1-24. - The Brownian continuum random tree
as the unique solution to a fixed point
equation, with Marie
Albenque,
*Electronic Communications in Probability***20**(2015), Paper no. 61, pp.1-14. - Behavior near the extinction time
in self-similar fragmentations II: Finite dislocation
measures, with Bénédicte Haas,
*Annals of Probability***44**, 1 (2016), pp.739-805. - A short introduction to random
trees,
*Mongolian Mathematical Journal***20**, 1 (2016), pp.53-72. - The scaling limit of the minimum
spanning
tree of the complete graph, with Louigi
Addario-Berry, Nicolas Broutin and Grégory
Miermont,
*Annals of Probability***45**, 5 (2017), pp.3075-3144. [Oberwolfach report]

Video of Louigi giving a talk about this work. - Voronoi
tessellations in the CRT and continuum random maps of finite
excess, with Louigi Addario-Berry, Omer Angel, Guillaume
Chapuy and Éric Fusy,
*Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)*(2018), pp.933-946.

Video of Omer giving a talk about this work. - Parking on a random tree,
with Michał Przykucki,
*Combinatorics, Probability and Computing***28**, 1 (2019), pp.23-45. - The spread of fire on a random multigraph,
with Eleonora
Kreačić,
*Advances in Applied Probability*,**51**, 1 (2019), pp.1-40. - Inverting the cut-tree transform, with
Louigi Addario-Berry and Daphné
Dieuleveut,
*Annales de l'Institut Henri Poincaré (Probabilités et Statistiques)*,**55**, 3 (2019), pp.1349-1376. - Scaling limits of random trees and
random graphs, in
*Random Graphs, Phase Transitions, and the Gaussian Free Field,*SSPROB 2017, Martin Barlow and Gordon Slade (eds.), Springer Proceedings in Mathematics & Statistics, vol 304. Springer, Cham (2020), pp.1-33.

[A full version of the proof of Theorem 16 sketched in these notes is given in this paper.] - Moderate deviations of subgraph counts in the
Erdős-Rényi random graphs G(n,m) and G(n,p), with
Simon Griffiths and Alex
Scott,
*Transactions of the American Mathematical Society*,**373**, 8 (2020), pp.5517-5585.

Video of Simon giving a talk about this work. - Parking on a random rooted plane
tree, with Qizhao
Chen,
*Bernoulli*,**27**, 1 (2021), pp.93-106. [arXiv 1911.03816] - Stable graphs: distributions
and line-breaking construction, with Bénédicte
Haas and Delphin
Sénizergues. [arXiv 1811.06940]

Video of me talking about this work. - The scaling limit of a critical random directed graph, with Robin Stephenson. [arXiv 1905.05397]
- The stable graph: the metric space
scaling limit of a critical random graph with i.i.d. power-law
degrees, with Guillaume
Conchon--Kerjan. [arXiv 2002.04954]

Video of me talking about this work, and video of Bénédicte talking about the companion paper 25, delivered at the One World Probability Seminar on 6th May 2021.

Mail to goldschm at stats.ox.ac.uk

Last modified: 9th May 2021.