Christina Goldschmidt

I am a University Lecturer in the Department of Statistics and a Tutorial Fellow at Lady Margaret Hall in the University of Oxford.

I did all of my studies at New Hall (now Murray Edwards College), University of Cambridge. I did my Ph.D. in the Statistical Laboratory with James Norris. I then spent a year (2003-4) working as a postdoc in the Laboratoire de Probabilités et Modèles Aléatoires at Université Paris VI with Jean Bertoin. From 2004 to 2007, I was the Stokes Fellow in Mathematics at Pembroke College, Cambridge. From 2007 to 2009, I held an EPSRC Postdoctoral Fellowship in the Department of Statistics at the University of Oxford. From 2009 to 2011, I was an Assistant Professor in the Department of Statistics at the University of Warwick. I spent the period from 8th March to 3rd April 2011 as professeur invité at Université Paris-Sud (Orsay).

My departmental office is 50.13 in the Medawar Building (number 37 on this map) and my telephone number is (01865) (2)81224. My college office is on the ground floor at the back of 2 Fyfield Road and my telephone number there is (01865) (2)74392. My official departmental webpage and my official college one.

Information about my teaching can be found on my teaching page. Some mathematical links can be found on my maths page and some non-work links can be found on my personal page.

Picture of me

As part of the Warwick EPSRC Symposium in Probability (academic year 2011-2012), Nathanaël Berestycki and I are organising a workshop entitled The Geometry of Discrete Random Structures, to take place 18th-22nd June 2012.

Research

My research interests lie in Probability and Combinatorics. I wrote my Ph.D. thesis on various aspects of the structure of random hypergraphs, with particular emphasis on the use of stochastic process methods. More recently, I have been working on scaling limits for various random graphs. I have also worked extensively on processes of coagulation (or coalescence) and fragmentation. Random trees and branching processes have played a large part in this research. I am particularly interested in the problem of duality for coagulation and fragmentation: when is the time-reversal of a coagulation process a "nice" fragmentation? I am also interested in applications of coalescence theory to mathematical population genetics. In a rather different direction, I am interested in random satisfiability problems, such as random K-SAT.

Talks

Slides from four lectures on random trees, random graphs and fragmentation processes given at Warwick in April 2009: Lecture 1, Lecture 2, Lecture 3, Lecture 4.

Slides and the handout from a lecture course given at the Young European Probabilists' Workshop on ``Probability, Random Trees and Algorithms'', EURANDOM, 8th-12th March 2010.

Slides from my talk at SPA in Oaxaca, 19th-24th July 2011.

Papers and articles

My Part III (approximately masters-level) essay entitled The Chen-Stein Method for Convergence of Distributions [.ps.gz (120kb)].
My PhD thesis entitled Large Random Hypergraphs [.ps.gz (747kb)].

Research papers:

  1. Essential edges in Poisson random hypergraphs, with James Norris, Random Structures and Algorithms 24, 4 (2004) pp.381-396.
    [.pdf, arXiv math.PR/0401143].
  2. Critical random hypergraphs: the emergence of a giant set of identifiable vertices, Annals of Probability 33, 4 (2005) pp.1573-1600.
    [.pdf, arXiv math.PR/0401208].
  3. 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.
    [.ps.gz, arXiv math.PR/0408128].
  4. Random recursive trees and the Bolthausen-Sznitman coalescent, with James Martin, Electronic Journal of Probability, 10 (2005), Paper no. 21, pp.718-745.
    [.pdf, arXiv math.PR/0502263].
  5. Preservation of log-concavity on summation, with Oliver Johnson, ESAIM: Probability and Statistics 10 (2006) pp.206-215.
    [.pdf, arXiv math.PR/05025848].
  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.
    [.pdf, arXiv math.PR/0507591].
  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.
    [.pdf, arXiv 0706.2808, extended abstract]
  8. Fragmenting random permutations, with James Martin and Dario Spanò, Electronic Communications in Probability 13 (2008), Paper no. 44, pp.461-474.
    [.pdf, arXiv 0712.0556]
  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.
    [.pdf, arXiv 0805.0967]
  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.
    [.pdf, arXiv 0908.3629]
  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.
    [.pdf, arXiv 1104.0983, Peter Windridge's simulation of Toth's random stirring model]
  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.
    [.pdf, arXiv 0903.4730]

My co-authors: Louigi Addario-Berry, Anne-Laure Basdevant, Jean Bertoin, Nicolas Broutin, Rui Dong, Bénédicte Haas, Olly Johnson, James Martin, James Norris, Dario Spanò, Daniel Ueltschi, Peter Windridge.
My Erdős number is 4.

Mail to goldschm at stats.ox.ac.uk
Last modified: 5th September 2011.