• Corpus ID: 221703085

# Airy Point Process via Supersymmetric Lifts

@article{Ahn2020AiryPP,
title={Airy Point Process via Supersymmetric Lifts},
author={Andrew Ahn},
journal={arXiv: Probability},
year={2020}
}
• Andrew Ahn
• Published 15 September 2020
• Mathematics
• arXiv: Probability
A supersymmetric lift of a symmetric function is a special sequence of doubly symmetric lifts which satisfies a cancellation property relating neighboring lifts in the sequence. We obtain contour integral formulas for observables of particle systems in terms of supersymmetric lifts of certain associated generating functions. We also obtain a family of supersymmetric lifts of multivariate Bessel functions and of Schur functions, along with contour integral formulas them. These formulas are…

## Figures from this paper

A Quantized Analogue of the Markov–Krein Correspondence
• Mathematics, Computer Science
International Mathematics Research Notices
• 2022
It is shown that the moment-generating function relationship induces a bijection between bounded measures and certain continual Young diagrams, which can be viewed as a quantized analogue of the Markov–Krein correspondence.
• Mathematics
• 2021
We consider fluctuations of the largest eigenvalues of the random matrix model A+ UBU∗ where A and B are (N ×N) deterministic Hermitian matrices and U is a Haar-distributed unitary matrix. Our main
Extremal singular values of random matrix products and Brownian motion on GL(N,C)
We establish universality for the largest singular values of products of random matrices with right unitarily invariant distributions, in a regime where the number of matrix factors and size of the
Matrix Addition and the Dunkl Transform at High Temperature
• Mathematics
Communications in Mathematical Physics
• 2022
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 the beta (inverse
Limits of Probability Measures With General Coefficients
With operators on formal series in $x_i$, $1\leq i\leq N$, which are symmetric in $N-1$ of the $x_i$, probability measures can be studied through Bessel generating functions. These operators are used
Operators on Bessel Generating Functions With General Coefficients UROP+ Final Paper, Summer 2021
• Mathematics
• 2021
With operators on formal series in xi, 1 ≤ i ≤ N , which are symmetric in N−1 of the xi, Bessel generating funtions can be studied. These operators are used with the Dunkl transform on Bessel
Universality of the least singular value for the sum of random matrices
• Mathematics
• 2019
We consider the least singular value of $M = R^* X T + U^* YV$, where $R,T,U,V$ are independent Haar-distributed unitary matrices and $X, Y$ are deterministic diagonal matrices. Under weak conditions

## References

SHOWING 1-10 OF 100 REFERENCES
Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory
• Mathematics
• 2015
We develop a new method for studying the asymptotics of symmetric polynomials of representation- theoretic origin as the number of variables tends to infinity. Several applications of our method are
A Determinantal Formula for Supersymmetric Schur Polynomials
• Mathematics
• 2003
We derive a new formula for the supersymmetric Schur polynomial sλ(x/y). The origin of this formula goes back to representation theory of the Lie superalgebra gl(m/n). In particular, we show how a
Representations of classical Lie groups and quantized free convolution
• Mathematics
• 2013
We study the decompositions into irreducible components of tensor products and restrictions of irreducible representations for all series of classical Lie groups as the rank of the group goes to
Supersymmetric Schur functions and Lie superalgebra representations
Lie superalgebras and their representations continue to play an important role in the understanding and exploitation of supersymmetry in physical systems. The Lie superalgebras that we consider,
Monotone Hurwitz Numbers and the HCIZ Integral
• Mathematics
• 2011
In this article, we study the topological expansion of the Harish-Chandra-Itzykson-Zuber matrix model. We prove three types of results concerning the free energy of the HCIZ model. First, at the
Moments Match between the KPZ Equation and the Airy Point Process
• Mathematics
• 2016
The results of Amir-Corwin-Quastel, Calabrese-Le Doussal-Rosso, Dotsenko, and Sasamoto-Spohn imply that the one-point distribution of the solution of the KPZ equation with the narrow wedge initial
Asymptotic fluctuations of representations of the unitary groups
• Mathematics
• 2009
We study asymptotics of representations of the unitary groups U(n) in the limit as n tends to infinity and we show that in many aspects they behave like large random matrices. In particular, we prove
Lozenge Tilings and Hurwitz Numbers
We give a new proof of the fact that, near a turning point of the frozen boundary, the vertical tiles in a uniformly random lozenge tiling of a large sawtooth domain are distributed like the
Universal edge fluctuations of discrete interlaced particle systems
• Mathematics
• 2017
We impose the uniform probability measure on the set of all discrete Gelfand-Tsetlin patterns of depth $n$ with the particles on row $n$ in deterministic positions. These systems equivalently