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Multicritical Schur Measures and Higher-Order Analogues of the Tracy–Widom Distribution
We introduce multicritical Schur measures, which are probability laws on integer partitions which give rise to non-generic fluctuations at their...
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Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices
We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom...
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Tracy-Widom Distributions for the Gaussian Orthogonal and Symplectic Ensembles Revisited: A Skew-Orthogonal Polynomials Approach
We study the distribution of the largest eigenvalue in the “Pfaffian” classical ensembles of random matrix theory, namely in the Gaussian orthogonal...
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Limiting Current Distribution for a Two Species Asymmetric Exclusion Process
We study current fluctuations of a two-species totally asymmetric exclusion process, known as the Arndt–Heinzel–Rittenberg model. For a...
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JT Gravity, Random Matrix Theoryand Third-Order Phase Transition
AbstractThe partition functions of Jackiw–Teitelboim (JT) gravity corresponds to random matrix integral. And we can define three different versions...
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Free Energy Fluctuations of the Bipartite Spherical SK Model at Critical Temperature
The spherical Sherrington–Kirkpatrick (SSK) model and its bipartite analog both exhibit the phenomenon that their free energy fluctuations are...
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Tracy–Widom Fluctuations in 2D Random Schrödinger Operators
We construct a random Schrödinger operator on a subset of the hexagonal lattice and study its smallest positive eigenvalues. Using an asymptotic...
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A Riemann Hilbert Approach to the Study of the Generating Function Associated to the Pearcey Process
Using Riemann–Hilbert methods, we establish a Tracy–Widom like formula for the generating function of the occupancy numbers of the Pearcey process....
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Semiclassical approach to form factors in the sinh-Gordon model
Form factors in the sinh-Gordon model are studied semiclassically for small values of the parameter b ~ ħ 1/2 in the background of a radial classical...
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Long and Short Time Asymptotics of the Two-Time Distribution in Local Random Growth
The two-time distribution gives the limiting joint distribution of the heights at two different times of a local 1D random growth model in the curved...
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Universal edge scaling in random partitions
We establish the universal edge scaling limit of random partitions with the infinite-parameter distribution called the Schur measure. We explore the...
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Unitary matrix models and random partitions: Universality and multi-criticality
The generating functions for the gauge theory observables are often represented in terms of the unitary matrix integrals. In this work, the...
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Shared Mathematical Content in the Context of Complex Systems
We pursue a reduction to the mathematical rather than a material content that is underlying a number of universal phenomena observed in different...
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Tracy–Widom Distributions in Critical Unitary Random Matrix Ensembles and the Coupled Painlevé II System
We study Fredholm determinants of the Painlevé II and Painlevé XXXIV kernels. In certain critical unitary random matrix ensembles, these determinants...
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Functional equations and separation of variables for exact g-function
The g -function is a measure of degrees of freedom associated to a boundary of two-dimensional quantum field theories. In integrable theories, it can...
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Universality of dissipative self-assembly from quantum dots to human cells
An important goal of self-assembly research is to develop a general methodology applicable to almost any material, from the smallest to the largest...
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Two-Point Convergence of the Stochastic Six-Vertex Model to the Airy Process
In this paper we consider the stochastic six-vertex model in the quadrant started with step initial data. After a long time T , it is known that the...
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Large Deformations of the Tracy–Widom Distribution I: Non-oscillatory Asymptotics
We analyze the left-tail asymptotics of deformed Tracy–Widom distribution functions describing the fluctuations of the largest eigenvalue in...
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Edge Distribution of Thinned Real Eigenvalues in the Real Ginibre Ensemble
This paper is concerned with the explicit computation of the limiting distribution function of the largest real eigenvalue in the real Ginibre...
