Research
* Preprints[21] N. Affolter, B. de Tilière, P. Melotti
The Schwarzian octahedron recurrence (dSKP equation) II: geometric systems.
arXiv: 2208.00244. 45 pages.
[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), no. 3-4, 451-462.
[2] B. de Tilière,
Scaling limit of isoradial dimer models and the case of triangular quadri-tilings. (arxiv version, title has changed)
Ann. Inst. H. Poincaré Sect. B. 43 no. 6 (2007), p. 729-750
[1] B. de Tilière,
Quadri-tilings of the plane.
Probab. Theory Related Fields, 137 (2007), no. 3-4, 487-518
* Lecture notes
The dimer model in statistical mechanics.
Dimer Models and Random Tilings. B. de Tiliè€re, P. Ferrari, edited by C. Boutillier, N. Enriquez. Panoramas et synthèses 45 (2015).
I have given lectures on this topic on the following occasions:
* 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