My name is Piet Lammers; I am a researcher and teacher in mathematical physics and particularly lattice models. I work as a junior professor in probability theory at LPSM within the Sorbonne Université in Paris, while being employed by CNRS. Before that I was a postdoc in the group of Hugo Duminil-Copin and a PhD student under the supervision of James Norris. Together with Yilin Wang and Thierry Bodineau, I organise the probability and analysis informal seminar at IHES.

Cours Peccot. I recently taught a Cours Peccot at Collège de France. I am still working on the lecture notes; the most recent version can be accessed via this link.

Research. Recent work focusses on the study of height functions in two dimensions. I study the phase transition associated to such height functions (called the localisation-delocalisation transition) and its relation to other phase transitions. Models which are mapped to height functions include: the Ising model, percolation (including Fortuin-Kasteleyn percolation), the classical XY model, and the loop O(2) model. I recently gave a talk which touches on several of my recent works; see this video.

The loop O(2) model The loop O(2) model

A very short CV.

Getting in touch. Please feel free to contact me by email at any time.

Photo by Patrick Imbert / Collège de France


Alexander Glazman, Peter van Hintum, Sébastien Ott, Martin Tassy, and Fabio Toninelli


  1. Delocalisation and continuity in 2D: loop O(2), six-vertex, and random-cluster models, with Alexander Glazman, preprint, pdf, bib.
  2. Bijecting the BKT transition, preprint, pdf, bib.
  3. A dichotomy theory for height functions, preprint, pdf, bib.
  4. Non-reversible stationary states for majority voter and Ising dynamics on trees, with Fabio Toninelli, preprint, pdf, bib.
  5. Macroscopic behavior of Lipschitz random surfaces, with Martin Tassy, Probab. Math. Phys. (2024), pdf, bib.
  6. Height function localisation on trees, with Fabio Toninelli, Combin. Probab. Comput. (2023), pdf, bib.
  7. Delocalisation and absolute-value-FKG in the solid-on-solid model, with Sébastien Ott, Probab. Theory Related Fields (2023), pdf, bib.
  8. Diffusivity of a walk on fracture loops of a discrete torus, Ann. Inst. Henri Poincaré Probab. Stat. (2023), pdf, bib.
  9. Height function delocalisation on cubic planar graphs, Probab. Theory Related Fields (2021), pdf, bib.
  10. A generalisation of the honeycomb dimer model to higher dimensions, Ann. Probab. (2021), pdf, bib.
  11. Variational principle for weakly dependent random fields, with Martin Tassy, J. Stat. Phys. (2020), pdf, bib.
  12. The bunkbed conjecture on the complete graph, with Peter van Hintum, European J. Combin. (2019), pdf, bib.


Recent Talks

International Congress in Mathematical Physics (Jul 2024, University of Strasbourg)
Workshop on Statistical Physics and Random Surfaces (May 2024, Oberwolfach)
Séminaire informel de probabilités du DMA (Apr 2024, ÉNS Paris)
Colloquium du MAP5 (Mar 2024, MAP5 — Université Paris Cité)
Statistical mechanics workshop (Feb 2024, SwissMAP Research Station)
Cours Peccot 4 (Feb 2024, Collège de France)
Cours Peccot 3 (Feb 2024, Collège de France)
Cours Peccot 2 (Jan 2024, Collège de France)
Cours Peccot 1 (Jan 2024, Collège de France)
Probability Seminar (Dec 2023, LPSM)



Fall 2022

  • Percolation

    Master2 at Paris-Saclay and IHES

    Tuesdays 14h00–16h00, Amphithéâtre Léon Motchane, IHES

    Start date: 20 September 2022

    Important dates.

    • The mid-term exam took place on 8 November from 14h00 until 17h00 at l'Institut de Mathématiques d'Orsay (bâtiment 307), salle 1A14.
    • The final exam took place on 17 January 2023 from 14h00 until 17h00 at l'Institut de Mathématiques d'Orsay (bâtiment 307), salle 1A11.
    • The last class took place on 10 January 2023. No new examinable material was presented.

    Contents. This course introduces the Bernoulli bond percolation model on the square lattice graph, as well as several modern techniques for analysing the model. The bond percolation model has a central place in statistical physics, and the ideas developed in the course find further applications in other models of statistical physics such as the Ising model, which will also be discussed if time permits. Paul Melotti will help with the exercise classes.

    Prerequisites. This is a course in probability theory. There are no prerequisites, but any intuition is useful: in particular, it will be helpful to have some experience with graphs and probability theory. Basic ideas on Galton-Watson trees (survival / extinction) will be reviewed at the start of the course.

    Schedule. The lectures consist of ten sessions of two hours each. Lectures are weekly in principle; any changes to the schedule will be announced during the lectures and on this webpage.

    Master thesis. Have a look at this thesis proposal if you are interested in writing a master thesis in percolation theory.

    Notes. Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 9 (lectured by Paul Melotti; original notes here), Exercises 1, Exam 1, Exam 2.

Contact details

Visiting address
Room 16-26.108
LPSM, Sorbonne Université
Campus Pierre et Marie Curie
4, place Jussieu
75005 Paris
Mail address
LPSM, Sorbonne Université
Campus Pierre et Marie Curie
Case courrier 158
4, place Jussieu
75252 Paris CEDEX 05
Email address