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.
arXiv: 2208.00239. 48
pages.
* Published/accepted papers
[19]
C. Boutillier, D. Cimasoni, B. de Tilière
Minimal bipartite
dimers and higher genus Harnack curves.
Accepted for publication (2022).
Probability and Mathematical Physics.
[18] C. Boutillier, D.
Cimasoni, B. de Tilière
Elliptic
dimers on minimal graphs and genus 1 Harnack curves
Accepted for publication (2022).
Comm.
Math. Phys.
[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,
[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:
- Master
2 Probabilités et Modèles Aléatoires, Université Pierre et
Marie Curie, Paris, 2013-.
- Etats de
la recherche, Institut Henri Poincaré, Paris, October 5-7,
2009.
- Swiss Doctoral Program in Mathematics and the EPFL doctoral
school: "Probability,
Statistical Mechanics", University of Neuchâtel, September
2008.
*
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.