Publications (21)
Matrix addition and the Dunkl transform at high temperature
Florent Benaych-Georges, Cesar Cuenca, Vadim Gorin
We develop a framework for establishing the Law of Large Numbers for the eigenvalues in the random matrix ensembles as the size of the matrix goes to infinity simultaneously with t…
Infinite-dimensional groups over finite fields and Hall-Littlewood symmetric functions
Cesar Cuenca, Grigori Olshanski
The groups mentioned in the title are certain matrix groups of infinite size over a finite field . They are built from finite classical groups and at the same time the…
q-deformed Character Theory for Infinite-Dimensional Symplectic and Orthogonal Groups
Cesar Cuenca, Vadim Gorin
The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalize…
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 of the ring of symmetric functions that are nonnegative on the images of certa…
Markov Processes on the Duals to Infinite-Dimensional Classical Lie Groups
Cesar Cuenca
We construct a four parameter (z, z', a, b) family of Markov dynamics that preserve the z-measures on the boundary of the branching graph for classical Lie groups of type B, C, D.…
Universal behavior of the corners of Orbital Beta Processes
Cesar Cuenca
There is a unique unitarily-invariant ensemble of Hermitian matrices with a fixed set of real eigenvalues . The joint eigenvalue distribution of the…
Laurent Phenomenon Sequences
Joshua Alman, Cesar Cuenca, Jiaoyang Huang
In this paper, we undertake a systematic study of recurrences x_{m+n}x_{m} = P(x_{m+1}, ..., x_{m+n-1}) which exhibit the Laurent phenomenon. Some of the most famous among these se…
Cumulants in rectangular finite free probability and beta-deformed singular values
Cesar Cuenca
Motivated by the -cumulants, introduced by Xu [arXiv:2303.13812] to study -deformed singular values of random matrices, we define the -rectangular cumulants for…
Mackey-type identity for invariant functions on Lie algebras of finite unitary groups and an application
Cesar Cuenca, Grigori Olshanski
The Mackey-type identity mentioned in the title relates the operations of parabolic induction and restriction for invariant functions on the Lie algebras of the finite unitary grou…
The Elliptic Tail Kernel
Cesar Cuenca, Vadim Gorin, Grigori Olshanski
We introduce and study a new family of -translation-invariant determinantal point processes on the two-sided -lattice. We prove that these processes are limits of the -$zw…
Interpolation Macdonald operators at infinity
Cesar Cuenca
We study the interpolation Macdonald functions, remarkable inhomogeneous generalizations of Macdonald functions, and a sequence of commuting operators that are d…
Universality of global asymptotics of Jack-deformed random Young diagrams at varying temperatures
Cesar Cuenca, Maciej DoÅÄga, Alexander Moll
This paper establishes universal formulas describing the global asymptotics of two distinct discrete versions of -ensembles in the high, low and fixed temperature regimes. Our…
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…
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…
Pieri Integral Formula and Asymptotics of Jack Unitary Characters
Cesar Cuenca
We introduce Jack (unitary) characters and prove two kinds of formulas that are suitable for their asymptotics, as the lengths of the signatures that parametrize them go to infinit…
Discrete -particle systems at high temperature through Jack generating functions
Cesar Cuenca, Maciej DoÅÄga
We find necessary and sufficient conditions for the Law of Large Numbers for random discrete -particle systems with the deformation (inverse temperature) parameter , as thei…
BC Type Z-measures and Determinantal Point Processes
Cesar Cuenca
The (BC type) z-measures are a family of four parameter probability measures on the path space of the nonnegative Gelfand-Tsetlin graph with Jacobi-edge multiplicitie…
Elements of the q-Askey scheme in the algebra of symmetric functions
Cesar Cuenca, Grigori Olshanski
The classical q-hypergeometric orthogonal polynomials are assembled into a hierarchy called the q-Askey scheme. At the top of the hierarchy, there are two closely related families,…
Asymptotic Formulas for Macdonald Polynomials and the Boundary of the -Gelfand-Tsetlin Graph
Cesar Cuenca
We introduce Macdonald characters and use algebraic properties of Macdonald polynomials to study them. As a result, we produce several formulas for Macdonald characters, which are…
Law of Large Numbers for continuous -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 -particle ensembles, in terms of the asymptotics of the…
Crystallization of discrete -particle systems at high temperature
Cesar Cuenca, Maciej DoÅÄga
This is the second paper in a series studying the global asymptotics of discrete -particle systems with inverse temperature parameter in the high temperature regime. In the…