• Corpus ID: 119123279

Random partitions and the quantum Benjamin-Ono hierarchy

  title={Random partitions and the quantum Benjamin-Ono hierarchy},
  author={Alexander Moll},
  journal={arXiv: Mathematical Physics},
  • Alexander Moll
  • Published 12 August 2015
  • Mathematics
  • arXiv: Mathematical Physics
Jack measures $M_V (\varepsilon_2, \varepsilon_1)$ on partitions $\lambda$ are discrete stochastic processes occurring naturally in the study of continuum circular $\beta$-ensembles in generic background potentials $V$ and arbitrary values $\beta$ of Dyson's inverse temperature. For analytic $V$, we prove a law of large numbers and central limit theorem in the scaling limit $\varepsilon_2 \rightarrow 0 \leftarrow \varepsilon_1$ taken at fixed inverse Jack parameter $\beta / 2=- \varepsilon_2… 
Law of Large Numbers and Central Limit Theorems by Jack Generating Functions
In a series of papers [22-24] by Bufetov and Gorin, Schur generating functions as the Fourier transforms on the unitary group $U(N)$, are introduced to study the asymptotic behaviors of random
Fine structure of moments of the KMK transform of the Poissonized Plancharel measure
We consider asymptotics behavior of Poissonized Plancharel measures as the poissonization parameter $N$ goes to infinity. Recently Moll proved a convergent series expansion for statistics of a
Gaussian Asymptotics of Jack Measures on Partitions from Weighted Enumeration of Ribbon Paths
In this paper we determine two asymptotic results for Jack measures on partitions, a model defined by two specializations of Jack polynomials proposed by Borodin-Olshanski in [European J. Combin.
Instanton R-matrix and $$ \mathcal{W} $$-symmetry
We study the relation between $\mathcal{W}_{1+\infty}$ algebra and Arbesfeld-Schiffmann-Tsymbaliuk Yangian using the Maulik-Okounkov R-matrix. The central object linking these two pictures is the
Fluctuations of interlacing sequences
In a series of works published in the 1990-s, Kerov put forth various applications of the circle of ideas centred at the Markov moment problem to the limiting shape of random continual diagrams
Exact Bohr-Sommerfeld Conditions for the Quantum Periodic Benjamin-Ono Equation
  • Alexander Moll
  • Mathematics
    Symmetry, Integrability and Geometry: Methods and Applications
  • 2019
In this paper we describe the spectrum of the quantum periodic Benjamin-Ono equation in terms of the multi-phase solutions of the underlying classical system (the periodic multi-solitons). To do so,
Finite gap conditions and small dispersion asymptotics for the classical periodic Benjamin–Ono equation
In this paper we characterize the Nazarov–Sklyanin hierarchy for the classical periodic Benjamin–Ono equation in two complementary degenerations: for the multiphase initial data (the periodic
Fluctuations of particle systems determined by Schur generating functions
Gaussian fluctuations of Jack-deformed random Young diagrams
We introduce a large class of random Young diagrams which can be regarded as a natural one-parameter deformation of some classical Young diagram ensembles; a deformation which is related to Jack


Quantum Geometry and Quiver Gauge Theories
We study macroscopically two dimensional $${\mathcal{N}=(2,2)}$$N=(2,2) supersymmetric gauge theories constructed by compactifying the quiver gauge theories with eight supercharges on a product
Kerov's central limit theorem for Schur-Weyl and Gelfand measures (extended abstract)
We show that the shapes of integer partitions chosen randomly according to Schur-Weyl measures of parameter $\alpha =1/2$ and Gelfand measures satisfy Kerov's central limit theorem. Thus, there is a
Large Deviations of the Maximum Eigenvalue
We here restrict ourselves to the case where V (x) = ?x 2/4 and for short denote by \(P_\beta ^N\) the law of the eigenvalues (?i)1?i?N: $$P_\beta ^N (d\lambda _1 , \cdots ,d\lambda _N ) =
Circular Jacobi Ensembles and Deformed Verblunsky Coefficients
Using the spectral theory of unitary operators and the theory of orthogonal polynomials on the unit circle, we propose a simple matrix model for the following circular analogue of the Jacobi
Macdonald processes
Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two Macdonald parameters $$q,t \in
Sekiguchi-Debiard Operators at Infinity
We construct a family of pairwise commuting operators such that the Jack symmetric functions of infinitely many variables $${x_1,x_2, \ldots}$$x1,x2,… are their eigenfunctions. These operators are
Global well-posedness in L2 for the periodic Benjamin-Ono equation
We prove that the Benjamin-Ono equation is globally well-posed in $ H^s({\Bbb T}) $ for $ s\ge 0 $. Moreover we show that the associated flow-map is Lipschitz on every bounded set of $ H^s_0({\Bbb
Gaussian asymptotics of discrete β$\beta $-ensembles
We introduce and study stochastic N$N$-particle ensembles which are discretizations for general-β$\beta $ log-gases of random matrix theory. The examples include random tilings, families of
Topological expansion of the Bethe ansatz, and quantum algebraic geometry
In this article, we solve the loop equations of the \beta-random matrix model, in a way similar to what was found for the case of hermitian matrices \beta=1. For \beta=1, the solution was expressed
Macdonald processes, quantum integrable systems and the Kardar-Parisi-Zhang universality class
Integrable probability has emerged as an active area of research at the interface of probability/mathematical physics/statistical mechanics on the one hand, and representation theory/integrable