Research

Papers in preparation

[24] C. Boutillier, B. Deb, B. de Tilière
Fock's dimer on Speyer graphs.

Submitted papers

[23] B. de Tilière, L. Rey
Classification of (non)-frustrated 2D Ising models in genus 1 on isoradial graphs.
arXiv:2602.13526, 92 pages.

Published / accepted papers

[22] C. Boutillier, B. de Tilière
Fock's dimer model on the Aztec diamond.
Accepted for publication. Ann. Inst. Poincaré D. (2026). arXiv:2405.20284, 51p.
[21] N. Affolter, B. de Tilière, P. Melotti
The Schwarzian octahedron recurrence (dSKP equation) II: geometric systems.
Discrete Comput. Geom. 73 (2025), 370-436.
[20] N. Affolter, B. de Tilière, P. Melotti
The Schwarzian octahedron recurrence (dSKP equation) I: explicit solutions.
Combin. Theory 3 (2023), no 2 #15, 1-58.
[19] C. Boutillier, D. Cimasoni, B. de Tilière
Minimal bipartite dimers and higher genus Harnack curves.
Probab. and Math. Phys. 4 (2023), 151-208.
[18] C. Boutillier, D. Cimasoni, B. de Tilière
Elliptic dimers on minimal graphs and genus 1 Harnack curves
Comm. Math. Phys. 400 (2023), 1071-1136.
[17] C. Boutillier, D. Cimasoni, B. de Tilière
Isoradial immersions
J. Graph Theory. 99 (2022), no 4, 715-757.
[16] B. de Tilière
The Z-Dirac and massive Laplacian operators in the Z-invariant Ising model
Electron. J. Probab. 26 (2021), paper no 53, 1-86.
[15] C. Boutillier, B. de Tilière, K. Raschel
The Z-invariant Ising model via dimers
Probab. Theory Related Fields. 174 (2019), no 1-2, 235-305.
[14] C. Boutillier, B. de Tilière, K. Raschel
The Z-invariant massive Laplacian on isoradial graphs
Invent. Math. 208 (2017), no 1, 109-189.
[13] B. de Tilière
Bipartite dimer representation of squared 2d-Ising correlations
Ann. Inst. H. Poincaré - Comb. Phys. Interact. 3 (2016), 121-138.
[12] B. de Tilière
Critical Ising model and spanning trees partition functions
Ann. Inst. H. Poincaré - Probab. et stat. 52 (2016), no 3, 1382-1405.
[11] C. Boutillier, B. de Tilière
Height representation of XOR-Ising loops via bipartite dimers.
Electron. J. Probab. 19 (2014), no 80, 1-33.
[10] B. de Tilière
Principal Minors Pfaffian Half-Tree Theorem.
J. Combin. Theory Ser. A. 124 (2014) 1-40.
[9] B. de Tilière
From cycle rooted spanning forests to the critical Ising model: an explicit construction.
Comm. Math. Phys. 319 (2013), no 1, 69-110.
[8] C. Boutillier, B. de Tilière
Statistical mechanics on isoradial graphs. (Survey paper)
Probability in Complex Physical Systems, in honour of Erwin Bolthausen and Jürgen Gärtner
Springer Proceedings in Mathematics 11 (2012) 491-512.
[7] C. Boutillier, B. de Tilière
The critical Z-invariant Ising model via dimers: locality property.
Comm. Math. Phys. 301 (2011), no 2, 473-516.
[6] C. Boutillier, B. de Tilière
The critical Z-invariant Ising model via dimers: the periodic case
Probab. Theory Related Fields, 147 (2010), 379-413.
[5] E. Bolthausen, F. Caravenna, B. de Tilière
The quenched critical point of a diluted disordered polymer model.
Stochastic Process. Appl. 119 (2009), 1479-1504.
[4] C. Boutillier, B. de Tilière
Loops statistics in the toroidal honeycomb dimer model.
Ann. Probab. 37 (2009), no 5, 1747-1777.
[3] B. de Tilière
Partition function of periodic isoradial dimer models.
Probab. Theory Related Fields, 138 (2007), 451-462.
[2] B. de Tilière
Scaling limit of isoradial dimer models and the case of triangular quadri-tilings.
Ann. Inst. H. Poincaré Sect. B 43 (2007), 729-750.
[1] B. de Tilière
Quadri-tilings of the plane.
Probab. Theory Related Fields, 137 (2007), 487-518.

Lecture notes

The dimer model in statistical mechanics.
In "Dimer Models and Random Tilings". B. de Tilière, P. Ferrari, edited by C. Boutillier, N. Enriquez.
Panoramas et synthèses 45, (2015). Société Mathématiques de France.

Habilitation thesis

Habilitation à diriger des recherches, Université Pierre et Marie Curie, Paris. November 2013.
Exactly solvable models of two-dimensional statistical mechanics: the Ising model, dimers and spanning trees.

PhD thesis

Université Paris XI, Orsay, December 2004.
Dimères sur les graphes isoradiaux & Modèle d'interfaces aléatoires en dimension 2+2.

Webpage of co-authors

Niklas Affolter, Erwin Bolthausen, Cédric Boutillier, Francesco Caravenna, Paul Melotti, Kilian Raschel