Cesar Cuenca

activity

20242026

collaborators

7 papers

math.PR2026

The Rectangular Finite Free Heat Flow

Cesar Cuenca, Colin McSwiggen

We define and study the rectangular finite free heat flow, a dynamical system on polynomials that plays the role of the heat equation in the setting of rectangular finite free prob…

math.CO2026

Hall-Littlewood-positive harmonic functionals on the algebra of symmetric functions

Cesar Cuenca, Grigori Olshanski

We study the problem of describing the set of real functionals on the quotient $Sym / (p_{2} - 1)$ of the ring of symmetric functions that are nonnegative on the images of certa…

math.PR2025

Law of Large Numbers for continuous $N$ -particle ensembles at fixed temperature

Cesar Cuenca, Jiaming Xu

In this paper, we find necessary and sufficient conditions for the Law of Large Numbers of averaged empirical measures of $N$ -particle ensembles, in terms of the asymptotics of the…

math-ph2025

Crystallization of discrete $N$ -particle systems at high temperature

Cesar Cuenca, Maciej Dołęga

This is the second paper in a series studying the global asymptotics of discrete $N$ -particle systems with inverse temperature parameter $θ$ in the high temperature regime. In the…

math.PR2025

Discrete $N$ -particle systems at high temperature through Jack generating functions

Cesar Cuenca, Maciej Dołęga

We find necessary and sufficient conditions for the Law of Large Numbers for random discrete $N$ -particle systems with the deformation (inverse temperature) parameter $θ$ , as their…

math.CO2024

Cumulants in rectangular finite free probability and beta-deformed singular values

Cesar Cuenca

Motivated by the $(q, γ)$ -cumulants, introduced by Xu [arXiv:2303.13812] to study $β$ -deformed singular values of random matrices, we define the $(n, d)$ -rectangular cumulants for po…

math-ph2024

The Symplectic Schur Process

Cesar Cuenca, Matteo Mucciconi

We define a measure on tuples of partitions, called the symplectic Schur process, that should be regarded as the right analogue of the Schur process of Okounkov-Reshetikhin for the…