3 citations · 5 across the 10 of their papers we have counts for
11 papers
Distribution of the roots of Eulerian polynomials
Paul Melotti
We give a new proof that the empirical measures of the roots of Eulerian polynomials converge to a certain log-Cauchy distribution. To do so, we show that each moment of the roots…
Local limit of massive spanning forests on the complete graph
Matteo D'Achille, Nathanaël Enriquez, Paul Melotti
We identify the local limit of massive spanning forests on the complete graph. This generalizes a well-known theorem of Grimmett on the local limit of uniform spanning trees on the…
The Schwarzian octahedron recurrence (dSKP equation) II: geometric systems
Niklas Christoph Affolter, Béatrice de Tilière, Paul Melotti
We consider nine geometric systems: Miquel dynamics, P-nets, integrable cross-ratio maps, discrete holomorphic functions, orthogonal circle patterns, polygon recutting, circle inte…
The Schwarzian octahedron recurrence (dSKP equation) I: explicit solutions
Niklas Christoph Affolter, Béatrice de Tilière, Paul Melotti
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 pa…
Points and lines configurations for perpendicular bisectors of convex cyclic polygons
Paul Melotti, Sanjay Ramassamy, Paul Thévenin
We characterize the topological configurations of points and lines that may arise when placing n points on a circle and drawing the n perpendicular bisectors of the sides of the co…
Cube moves for -embeddings and -realizations
Paul Melotti, Sanjay Ramassamy, Paul Thévenin
Chelkak introduced -embeddings as tilings by tangential quads which provide the right setting to study the Ising model with arbitrary coupling constants on arbitrary planar grap…
The free-fermion eight-vertex model: couplings, bipartite dimers and Z-invariance
Paul Melotti
We study the eight-vertex model at its free-fermion point. We express a new "switching" symmetry of the model in several forms: partition functions, order-disorder variables, coupl…
On path partitions of the divisor graph
Paul Melotti, Eric Saias
It is known that the longest simple path in the divisor graph that uses integers is of length . We study the partitions of into a minim…
The free-fermionic loop model, double dimers and Kashaev's recurrence
Paul Melotti
We study a two-color loop model known as the loop model. We define a free-fermionic regime for this model, and show that under this assumption it can be transformed int…
A probabilistic Hadwiger-Nelson problem
Thomas Bourgeat, Marc Heinrich, Paul Melotti +1
If you color a table using k colors, and throw a needle randomly on it, for some proper definition, you get a certain probability that the endpoints will fall on different colors.…
New Algorithmic Approaches to Point Constellation Recognition
Thomas Bourgeat, Julien Bringer, Herve Chabanne +7
Point constellation recognition is a common problem with many pattern matching applications. Whilst useful in many contexts, this work is mainly motivated by fingerprint matching.…