Research

* Preprints

[17] C. Boutillier, D. Cimasoni, B. de Tilière
Isoradial immersions

arXiv:1912.10297. 44 pages.


[16] B. de Tilière
The Z-Dirac and massive Laplacian operators in the Z-invariant Ising model

arXiv:1801.00207
. 103 pages.

* Published/accepted papers

[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 Tilière, 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

Erwin Bolthausen Cédric Boutillier Francesco Caravenna Kilian Raschel