22 citations · 106 across the 24 of their papers we have counts for
24 papers
Multiple cluster algebra structures for TCD maps I: theoretical framework
Niklas Affolter, Terrence George, Max Glick +1
We introduce triple crossing diagram (TCD) maps, which encode projective configurations of points and lines, as a unified framework for constructions arising in various areas of ge…
Wall-crossing phenomenon for the liquid bin model
Sanjay Ramassamy, Benjamin Terlat
We introduce the liquid bin model as a continuous-time deterministic dynamics, arising as the hydrodynamic limit of a discrete-time stochastic interacting particle system called th…
Freezing in the Infinite-Bin Model
Bastien Mallein, Sanjay Ramassamy, Arvind Singh
The infinite-bin model is a one-dimensional particle system on introduced by Foss and Konstantopoulos in relation with last passage percolation on complete directed ac…
Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models
Sergey Foss, Takis Konstantopoulos, Bastien Mallein +1
We consider directed random graphs, the prototype of which being the Barak-Erdős graph , and study the way that long (or heavy, if weights are present) paths…
Discrete dynamics in cluster integrable systems from geometric -matrix transformations
Terrence George, Sanjay Ramassamy
Cluster integrable systems are a broad class of integrable systems modelled on bipartite dimer models on the torus. Many discrete integrable dynamics arise by applying sequences of…
Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation
Sergey Foss, Takis Konstantopoulos, Bastien Mallein +1
Our object of study is the asymptotic growth of heaviest paths in a charged (weighted with signed weights) complete directed acyclic graph. Edge charges are i.i.d. random variables…
Integrable dynamics in projective geometry via dimers and triple crossing diagram maps on the cylinder
Niklas Christoph Affolter, Terrence George, Sanjay Ramassamy
We introduce twisted triple crossing diagram maps, collections of points in projective space associated to bipartite graphs on the cylinder, and use them to provide geometric reali…
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…
Fluctuations in the Aztec diamonds via a space-like maximal surface in Minkowski 3-space
Dmitry Chelkak, Sanjay Ramassamy
We provide a new description of the scaling limit of dimer fluctuations in homogeneous Aztec diamonds via the intrinsic conformal structure of a space-like maximal surface in the t…
Vector-relation configurations and plabic graphs
Niklas Affolter, Max Glick, Pavlo Pylyavskyy +1
We study a simple geometric model for local transformations of bipartite graphs. The state consists of a choice of a vector at each white vertex made in such a way that the vectors…
The Foata correspondence, cycle lengths and anomalies
Sanjay Ramassamy
In their study of the densest jammed configurations for theater models, Krapivsky and Luck observe that two classes of permutations have the same cardinalities and ask for a biject…
Dimers and Circle patterns
Richard Kenyon, Wai Yeung Lam, Sanjay Ramassamy +1
We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar…
Laminations of a graph on a pair of pants
Sanjay Ramassamy
A lamination of a graph embedded on a surface is a collection of pairwise disjoint non-contractible simple closed curves drawn on the graph. In the case when the surface is a spher…
Extensions of partial cyclic orders and consecutive coordinate polytopes
Arvind Ayyer, Matthieu Josuat-Vergès, Sanjay Ramassamy
We introduce several classes of polytopes contained in and cut out by inequalities involving sums of consecutive coordinates. We show that the normalized volumes of these…
A first integrability result for Miquel dynamics
Alexey Glutsyuk, Sanjay Ramassamy
Miquel dynamics is a discrete-time dynamical system on the space of square-grid circle patterns. For biperiodic circle patterns with both periods equal to two, we show that the dyn…
Modular periodicity of the Euler numbers and a sequence by Arnold
Sanjay Ramassamy
For any positive integer , the sequence of the Euler up/down numbers reduced modulo was proved to be ultimately periodic by Knuth and Buckholtz. Based on computer simulation…
Two-sided infinite-bin models and analyticity for Barak-Erdős graphs
Bastien Mallein, Sanjay Ramassamy
In this article, we prove that for any probability distribution on one can construct a two-sided stationary version of the infinite-bin model (an interacting parti…
The Hilbert-Galton board
Arvind Ayyer, Sanjay Ramassamy
We introduce the Hilbert-Galton board as a variant of the classical Galton board. Balls fall into a row of bins at a rate depending on the bin, and at random times, each bin gets s…
Miquel dynamics for circle patterns
Sanjay Ramassamy
We study a new discrete-time dynamical system on circle patterns with the combinatorics of the square grid. This dynamics, called Miquel dynamics, relies on Miquel's six circles th…
Extensions of partial cyclic orders, Euler numbers and multidimensional boustrophedons
Sanjay Ramassamy
We enumerate total cyclic orders on where we prescribe the relative cyclic order of consecutive triples , these integers being taken mo…
Barak-Erdős graphs and the infinite-bin model
Bastien Mallein, Sanjay Ramassamy
A Barak-Erdős graph is a directed acyclic version of the Erdős-Rényi random graph. It is obtained by performing independent bond percolation with parameter on the complete grap…
Coupling any number of balls in the infinite-bin model
Ksenia Chernysh, Sanjay Ramassamy
The infinite-bin model, introduced by Foss and Konstantopoulos, describes the Markovian evolution of configurations of balls placed inside bins, obeying certain transition rules. W…
Dimers on Rail Yard Graphs
Cédric Boutillier, Jérémie Bouttier, Guillaume Chapuy +2
We introduce a general model of dimer coverings of certain plane bipartite graphs, which we call rail yard graphs (RYG). The transfer matrices used to compute the partition functio…