Cédric Boutillier

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In this paper, we study the bead model : beads are threaded on a set of wires on the plane represented by parallel straight lines. We add the constraint that between two consecutive beads on a wire, there must be exactly one bead on each neighboring wire. We construct a one-parameter family of Gibbs measures on the bead configurations that are uniform in a(More)
We study a large class of critical two-dimensional Ising models namely critical Z-invariant Ising models on periodic graphs, example of which are the classical Z, triangular and honeycomb lattice at the critical temperature. Fisher [Fis66] introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer(More)
We study a large class of critical two-dimensional Ising models, namely critical Z-invariant Ising models. Fisher [Fis66] introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dimer(More)
Let G be a graph. A dimer configuration C of a graph G is a subset of edges of G such that every vertex of G is incident to exactly one edge of C. The dimer model is a system from statistical mechanics, obtained by endowing the set of all possible dimer configurations with a probability measure. It has been introduced in the 1930s [3] to give a model for(More)
We introduce a one-parameter family of massive Laplacian operators (∆)k∈[0,1) defined on isoradial graphs, involving elliptic functions. We prove an explicit formula for minus the inverse of ∆, the massive Green function, which has the remarkable property of only depending on the local geometry of the graph, and compute its asymptotics. We study the(More)
We describe random generation algorithms for a large class of random combinatorial objects called Schur processes, which are sequences of random (integer) partitions subject to certain interlacing conditions. This class contains several fundamental combinatorial objects as special cases, such as plane partitions, tilings of Aztec diamonds, pyramid(More)
Isoradial graphs are a natural generalization of regular graphs which give, for many models of statistical mechanics, the right framework for studying models at criticality. In this survey paper, we first explain how isoradial graphs naturally arise in two approaches used by physicists: transfer matrices and conformal field theory. This leads us to the fact(More)
Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes. In the present work, we consider the limit of large random skew plane partitions where the inner boundary approaches a piecewise linear curve with non-lattice slopes, describing the limit shape and the local fluctuations in various(More)
The authors report the case of a 38 year old sportsman who received a football in the centre of his chest during a football match. Over the following minutes, he experienced a mid-thoracic pain which corresponded to the development of a myocardial infarction which was secondarily complicated by left ventricular failure. Ventriculography revealed a large(More)