Christina Goldschmidt: publications

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

1. Essential edges in Poisson random hypergraphs, with James Norris, Random Structures and Algorithms 24, 4 (2004) pp.381-396.


2. 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.


3. Critical random hypergraphs: the emergence of a giant set of identifiable vertices, Annals of Probability 33, 4 (2005) pp.1573-1600.


4. 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].


5. Preservation of log-concavity on summation, with Oliver Johnson, ESAIM: Probability and Statistics 10 (2006) pp.206-215.


6. 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.


7. 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]


8. Fragmenting random permutations, with James Martin and Dario Spanò, Electronic Communications in Probability 13 (2008), Paper no. 44, pp.461-474.


9. 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)


10. 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.


11. 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.


12. 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.]


13. A line-breaking construction of the stable trees, with Bénédicte Haas, Electronic Journal of Probability 20 (2015), Paper no. 16, pp.1-24.


14. 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.
    


15. 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.


16. A short introduction to random trees, Mongolian Mathematical Journal 20, 1 (2016), pp.53-72.


17. 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]
    [Erratum: on p.3111, just after equation (4.12), we claim that Theorem A1 of [40] gives a bound on the relevant expected value, whereas it in fact only gives a bound in probability. A proof may be found in Proposition 3.8 of Blanc-Renaudie, Broutin and Nachmias, The scaling limit of hypercube percolation.]
    Video of Louigi giving a talk about this work.


18. 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.


19. Parking on a random tree, with Michał Przykucki, Combinatorics, Probability and Computing 28, 1 (2019), pp.23-45.


20. The spread of fire on a random multigraph, with Eleonora Kreačić, Advances in Applied Probability, 51, 1 (2019), pp.1-40.


21. 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.


22. 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.]


23. 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.


24. Parking on a random rooted plane tree, with Qizhao Chen, Bernoulli, 27, 1 (2021), pp.93-106.


25. Stable graphs: distributions and line-breaking construction, with Bénédicte Haas and Delphin Sénizergues, Annales Henri Lebesgue 5 (2022), pp.841-904.
    Video of me talking about this work.


26. The stable graph: the metric space scaling limit of a critical random graph with i.i.d. power-law degrees, with Guillaume Conchon--Kerjan, Annals of Probability 51, 1 (2023), pp.1-69
    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.


27. The scaling limit of a critical random directed graph, with Robin Stephenson, Annals of Applied Probability 33 (2023), pp.2024-2065.


28. A large deviation principle for the normalized excursion of α-stable Lévy processes without negative jumps, with Léo Dort and Grégory Miermont, ALEA, Latin American Journal of Probability and Mathematical Statistics 21, 2 (2024), pp.1625-1653.


29. Scaling limits of random graphs, with Louigi Addario-Berry, to appear in the volume Topics in Probabilistic Graph Theory.