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pro vyhledávání: '"De Tilière, Béatrice"'
We consider the dimer model on the Aztec diamond with Fock's weights, which is gauge equivalent to the model with any choice of positive weight function. We prove an explicit, compact formula for the inverse Kasteleyn matrix, thus extending numerous
Externí odkaz:
http://arxiv.org/abs/2405.20284
Publikováno v:
Discrete Comput Geom (2024)
We consider nine geometric systems: Miquel dynamics, P-nets, integrable cross-ratio maps, discrete holomorphic functions, orthogonal circle patterns, polygon recutting, circle intersection dynamics, (corrugated) pentagram maps and the short diagonal
Externí odkaz:
http://arxiv.org/abs/2208.00244
We prove an explicit expression for the solutions of the discrete Schwarzian octahedron recurrence, also known as the discrete Schwarzian KP equation (dSKP), as the ratio of two partition functions. Each one counts weighted oriented dimer configurati
Externí odkaz:
http://arxiv.org/abs/2208.00239
Publikováno v:
Prob. Math. Phys. 4 (2023) 151-208
This paper completes the comprehensive study of the dimer model on infinite minimal graphs with Fock's weights [arXiv:1503.00289] initiated in [arXiv:2007.14699]: the latter article dealt with the elliptic case, i.e., models whose associated spectral
Externí odkaz:
http://arxiv.org/abs/2112.12622
This paper provides a comprehensive study of the dimer model on infinite minimal graphs with Fock's elliptic weights [arXiv:1503.00289]. Specific instances of such models were studied in [arXiv:052711, arXiv:1612.09082, arXiv1801.00207]; we now handl
Externí odkaz:
http://arxiv.org/abs/2007.14699
Isoradial embeddings of planar graphs play a crucial role in the study of several models of statistical mechanics, such as the Ising and dimer models. Kenyon and Schlenker give a combinatorial characterization of planar graphs admitting an isoradial
Externí odkaz:
http://arxiv.org/abs/1912.10297
Autor:
de Tilière, Béatrice
Consider an elliptic parameter $k$; we introduce a family of $Z^u$-Dirac operators $(\mathsf{K}(u))_{u\in\Re(\mathbb{T}(k))}$, relate them to the $Z$-massive Laplacian of [BdTR17b], and extend to the full $Z$-invariant case the results of Kenyon [Ken
Externí odkaz:
http://arxiv.org/abs/1801.00207
Publikováno v:
Probability Theory and Related Fields 174 (2019) 235-305
The $Z$-invariant Ising model (Baxter in Philos Trans R Soc Lond A Math Phys Eng Sci 289(1359):315--346, 1978) is defined on an isoradial graph and has coupling constants depending on an elliptic parameter $k$. When $k=0$ the model is critical, and a
Externí odkaz:
http://arxiv.org/abs/1612.09082
Autor:
De Tilière, Béatrice
Ce mémoire donne un aperçu de mes travaux de recherche depuis la thèse. La thématique générale est la mécanique statistique, qui a pour but de comprendre le comportement macroscopique d'un système physique dont les interactions sont décrites
Externí odkaz:
http://tel.archives-ouvertes.fr/tel-00909569
http://tel.archives-ouvertes.fr/docs/00/90/95/69/PDF/memoire.pdf
http://tel.archives-ouvertes.fr/docs/00/90/95/69/PDF/memoire.pdf
Publikováno v:
Inventiones mathematicae April 2017, Volume 208, Issue 1, pp 109-189
We introduce a one-parameter family of massive Laplacian operators $(\Delta^{m(k)})_{k\in[0,1)}$ defined on isoradial graphs, involving elliptic functions. We prove an explicit formula for the inverse of $\Delta^{m(k)}$, the massive Green function, w
Externí odkaz:
http://arxiv.org/abs/1504.00792