Sanjay Ramassamy
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Sanjay Ramassamy has a total of 18 co-authors. Here are the top co-authors by number of shared publications:
- Bastien Mallein
Univ Sorbonne Paris Nord, LAGA, UMR 7539, F-93430 Villetaneuse, France
3 shared publications - Sergey Foss
Heriot-Watt University, Edinburgh, UK
2 shared publications - Takis Konstantopoulos
Department of Mathematics Uppsala University
2 shared publications - Arvind Singh
CNRS and LMO, Université Paris-Saclay
1 shared publication - Bastien Mallein
Institut de Mathématiques de Toulouse UMR 5219 Université de Toulouse France
1 shared publication France Université Paris-Saclay
1 shared publication
Latest Publications
- Open Access
Multiple cluster algebra structures for TCD maps I: theoretical framework
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 geometry, such as discrete differential geometry, discrete geometric dynamics and hyperbolic geometry. We define two types of local moves for TCD maps, one of which is governed by the discrete Schwarzian KP (dSKP) equation, and establish their multi-dimensional consistency. We construct two distinct cluster structures on the space of TCD maps, called projective and affine cluster structures, and show that they are related via an operation called section. This framework organizes and unifies a wide range of examples, including Q-nets, Darboux maps, line complexes, T-graphs, t-embeddings, triangulations and geometric discrete integrable systems such as the pentagram map and cross-ratio dynamics, which are further developed in a companion paper and in (arXiv:2108.12692).
Open AccessMultiple cluster algebra structures for TCD maps I: theoretical framework
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 geometry, such as discrete differential geometry, discrete geometric dynamics and hyperbolic geometry. We define two types of local moves for TCD maps, one of which is governed by the discrete Schwarzian KP (dSKP) equation, and establish their multi-dimensional consistency. We construct two distinct cluster structures on the space of TCD maps, called projective and affine cluster structures, and show that they are related via an operation called section. This framework organizes and unifies a wide range of examples, including Q-nets, Darboux maps, line complexes, T-graphs, t-embeddings, triangulations and geometric discrete integrable systems such as the pentagram map and cross-ratio dynamics, which are further developed in a companion paper and in (arXiv:2108.12692).
- Open Access
- 3 June 2025
- Published by SIGMA (Symmetry, Integrability and Geometry: Methods and Application) in Symmetry, Integrability and Geometry: Methods and Applications
- Vol. 21, 040
Integrable Dynamics in Projective Geometry via Dimers and Triple Crossing Diagram Maps on the Cylinder
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 realizations of the cluster integrable systems of Goncharov and Kenyon constructed from toric dimer models. Using this notion, we provide geometric proofs that the pentagram map and the cross-ratio dynamics integrable systems are cluster integrable systems. We show that in appropriate coordinates, cross-ratio dynamics is described by geometric $R$-matrices, which solves the open question of finding a cluster algebra structure describing cross-ratio dynamics.
- 3 June 2025
- Published by SIGMA (Symmetry, Integrability and Geometry: Methods and Application) in Symmetry, Integrability and Geometry: Methods and Applications
- Vol. 21, 040
Open AccessIntegrable Dynamics in Projective Geometry via Dimers and Triple Crossing Diagram Maps on the Cylinder
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 realizations of the cluster integrable systems of Goncharov and Kenyon constructed from toric dimer models. Using this notion, we provide geometric proofs that the pentagram map and the cross-ratio dynamics integrable systems are cluster integrable systems. We show that in appropriate coordinates, cross-ratio dynamics is described by geometric $R$-matrices, which solves the open question of finding a cluster algebra structure describing cross-ratio dynamics.
- Open Access
Freezing in the Infinite-Bin Model
The infinite-bin model is a one-dimensional particle system on Z introduced by Foss and Konstantopoulos in relation with last passage percolation on complete directed acyclic graphs. In this model, at each integer time, a particle is selected at random according to its rank, and produces a child at the location immediately to its right. In this article, we consider the limiting distribution of particles after an infinite number of branching events have occurred. Under mild assumptions, we prove that the event (called freezing) that a location contains only a finite number of balls satisfies a 0-1 law and we provide various criteria to determine whether freezing occurs.
Open AccessFreezing in the Infinite-Bin Model
The infinite-bin model is a one-dimensional particle system on Z introduced by Foss and Konstantopoulos in relation with last passage percolation on complete directed acyclic graphs. In this model, at each integer time, a particle is selected at random according to its rank, and produces a child at the location immediately to its right. In this article, we consider the limiting distribution of particles after an infinite number of branching events have occurred. Under mild assumptions, we prove that the event (called freezing) that a location contains only a finite number of balls satisfies a 0-1 law and we provide various criteria to determine whether freezing occurs.
- Top Cited Papers
- 21 December 2023
- Published by Springer Nature in Selecta Mathematica
- Vol. 30 (1) , 1-55
Vector-relation configurations and plabic graphs
- 21 December 2023
- Published by Springer Nature in Selecta Mathematica
- Vol. 30 (1) , 1-55
Top Cited PapersVector-relation configurations and plabic graphs
- Open Access
Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation
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 with common distribution $F$ supported on $[-\infty,1]$ with essential supremum equal to $1$ (a charge of $-\infty$ is understood as the absence of an edge). The asymptotic growth rate is a constant that we denote by $C(F)$. Even in the simplest case where $F=p\delta_1 + (1-p)\delta_{-\infty}$, corresponding to the longest path in the Barak-Erd\H{o}s random graph, there is no closed-form expression for this function, but good bounds do exist. In this paper we construct a Markovian particle system that we call "Max Growth System" (MGS), and show how it is related to the charged random graph. The MGS is a generalization of the Infinite Bin Model that has been the object of study of a number of papers. We then identify a random functional of the process that admits a stationary version and whose expectation equals the unknown constant $C(F)$. Furthermore, we construct an effective perfect simulation algorithm for this functional which produces samples from the random functional.Open AccessEstimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation
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 with common distribution $F$ supported on $[-\infty,1]$ with essential supremum equal to $1$ (a charge of $-\infty$ is understood as the absence of an edge). The asymptotic growth rate is a constant that we denote by $C(F)$. Even in the simplest case where $F=p\delta_1 + (1-p)\delta_{-\infty}$, corresponding to the longest path in the Barak-Erd\H{o}s random graph, there is no closed-form expression for this function, but good bounds do exist. In this paper we construct a Markovian particle system that we call "Max Growth System" (MGS), and show how it is related to the charged random graph. The MGS is a generalization of the Infinite Bin Model that has been the object of study of a number of papers. We then identify a random functional of the process that admits a stationary version and whose expectation equals the unknown constant $C(F)$. Furthermore, we construct an effective perfect simulation algorithm for this functional which produces samples from the random functional. - 14 February 2023
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions
- Vol. 10 (4) , 781-817
Cube moves for $s$-embeddings and $\alpha$-realizations
Chelkak introduced $s$-embeddings as tilings by tangential quads which provide the right setting to study the Ising model with arbitrary coupling constants on arbitrary planar graphs. We prove the existence and uniqueness of a local transformation for $s$-embeddings called the cube move, which consists in flipping three quadrilaterals in such a way that the resulting tiling is also in the class of $s$-embeddings. In passing, we give a new and simpler formula for the change in coupling constants for the Ising star-triangle transformation which is conjugated to the cube move for $s$-embeddings. We introduce more generally the class of $\alpha$-embeddings as tilings of a portion of the plane by quadrilaterals such that the side lengths of each quadrilateral $ABCD$ satisfy the relation $AB^\alpha+CD^\alpha=AD^\alpha+BC^\alpha$, providing a common generalization for harmonic embeddings adapted to the study of resistor networks ($\alpha=2$) and for $s$-embeddings ($\alpha=1$). We investigate existence and uniqueness properties of the cube move for these $\alpha$-embeddings.- 14 February 2023
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions
- Vol. 10 (4) , 781-817
Cube moves for $s$-embeddings and $\alpha$-realizations
Chelkak introduced $s$-embeddings as tilings by tangential quads which provide the right setting to study the Ising model with arbitrary coupling constants on arbitrary planar graphs. We prove the existence and uniqueness of a local transformation for $s$-embeddings called the cube move, which consists in flipping three quadrilaterals in such a way that the resulting tiling is also in the class of $s$-embeddings. In passing, we give a new and simpler formula for the change in coupling constants for the Ising star-triangle transformation which is conjugated to the cube move for $s$-embeddings. We introduce more generally the class of $\alpha$-embeddings as tilings of a portion of the plane by quadrilaterals such that the side lengths of each quadrilateral $ABCD$ satisfy the relation $AB^\alpha+CD^\alpha=AD^\alpha+BC^\alpha$, providing a common generalization for harmonic embeddings adapted to the study of resistor networks ($\alpha=2$) and for $s$-embeddings ($\alpha=1$). We investigate existence and uniqueness properties of the cube move for these $\alpha$-embeddings.- Open Access
Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation
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 with common distribution $F$ supported on $[−\infty, 1$] with essential supremum equal to 1 (a charge of $−\infty$ is understood as the absence of an edge). The asymptotic growth rate is a constant that we denote by $C(F)$. Even in the simplest case where $F = p\delta_1 + (1 − p)\delta_{-\infty}$, corresponding to the longest path in the Barak-Erdős random graph, there is no closed-form expression for this function, but good bounds do exist. In this paper we construct a Markovian particle system that we call "Max Growth System" (MGS), and show how it is related to the charged random graph. The MGS is a generalization of the Infinite Bin Model that has been the object of study of a number of papers. We then identify a random functional of the process that admits a stationary version and whose expectation equals the unknown constant $C(F)$. Furthermore, we construct an effective perfect simulation algorithm for this functional which produces samples from the random functional.Open AccessEstimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation
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 with common distribution $F$ supported on $[−\infty, 1$] with essential supremum equal to 1 (a charge of $−\infty$ is understood as the absence of an edge). The asymptotic growth rate is a constant that we denote by $C(F)$. Even in the simplest case where $F = p\delta_1 + (1 − p)\delta_{-\infty}$, corresponding to the longest path in the Barak-Erdős random graph, there is no closed-form expression for this function, but good bounds do exist. In this paper we construct a Markovian particle system that we call "Max Growth System" (MGS), and show how it is related to the charged random graph. The MGS is a generalization of the Infinite Bin Model that has been the object of study of a number of papers. We then identify a random functional of the process that admits a stationary version and whose expectation equals the unknown constant $C(F)$. Furthermore, we construct an effective perfect simulation algorithm for this functional which produces samples from the random functional. - Open Access
Barak-Erdős graphs and the infinite-bin model
A Barak-Erd\H{o}s graph is a directed acyclic version of the Erd\H{o}s-R\'enyi random graph. It is obtained by performing independent bond percolation with parameter $p$ on the complete graph with vertices $\{1,...,n\}$, in which the edge between two vertices $i1/2$, and compute its power series expansion. We also obtain the first two terms of the asymptotic expansion of $C$ as $p \to 0$, using a coupling with branching random walks.Open AccessBarak-Erdős graphs and the infinite-bin model
A Barak-Erd\H{o}s graph is a directed acyclic version of the Erd\H{o}s-R\'enyi random graph. It is obtained by performing independent bond percolation with parameter $p$ on the complete graph with vertices $\{1,...,n\}$, in which the edge between two vertices $i1/2$, and compute its power series expansion. We also obtain the first two terms of the asymptotic expansion of $C$ as $p \to 0$, using a coupling with branching random walks. - 28 June 2020
- Published by Wiley in Bulletin of the London Mathematical Society
- Vol. 52 (6) , 1038-1052
Laminations of a graph on a pair of pants
- 28 June 2020
- Published by Wiley in Bulletin of the London Mathematical Society
- Vol. 52 (6) , 1038-1052
Laminations of a graph on a pair of pants