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Sho Matsumoto

Publications and source records attributed to Sho Matsumoto.

At least 37 records · Page 2Linked to original sources
arXiv2021

OGLE-2014-BLG-0319: A Sub-Jupiter-Mass Planetary Event Encountered Degeneracy with Different Mass Ratios and Lens-Source Relative Proper Motions

We report the discovery of a sub-Jovian-mass planet, OGLE-2014-BLG-0319Lb. The characteristics of this planet will be added into a future extended statistical analysis of the Microlensing Observations in Astrophysics (MOA) collaboration. The planetary anomaly of the light curve is characterized by MOA and OGLE survey observations and results in three degenerate models with different planetary mass-ratios of $q=(10.3,6.6,4.5)\times10^{-4}$, respectively. We find that the last two models require unreasonably small lens-source relative proper motions of $μ_{\rm rel}\sim1\;{\rm mas/yr}$. Considering Galactic prior probabilities, we rule out these two models from the final result. We conduct a Bayesian analysis to estimate physical properties of the lens system using a Galactic model and find that the lens system is composed of a $0.49^{+0.35}_{-0.27}\;M_{\rm Jup}$ sub-Jovian planet orbiting a $0.47^{+0.33}_{-0.25}\; M_{\odot}$ M-dwarf near the Galactic bulge. This analysis demonstrates that Galactic priors are useful to resolve this type of model degeneracy. This is important for estimating the mass ratio function statistically. However, this method would be unlikely successful in shorter timescale events, which are mostly due to low-mass objects, like brown dwarfs or free-floating planets. Therefore, careful treatment is needed for estimating the mass ratio function of the companions around such low-mass hosts which only the microlensing can probe.

astro-ph.EP↗
arXiv2021

KMT-2021-BLG-0912Lb: A microlensing super Earth around a K-type star

The light curve of the microlensing event KMT-2021-BLG-0912 exhibits a very short anomaly relative to a single-lens single-source form. We investigate the light curve for the purpose of identifying the origin of the anomaly. We model the light curve under various interpretations. From this, we find four solutions, in which three solutions are found under the assumption that the lens is composed of two masses (2L1S models), and the other solution is found under the assumption that the source is comprised of a binary-star system (1L2S model). The 1L2S model is ruled out based on the contradiction that the faint source companion is bigger than its primary, and one of the 2L1S solutions is excluded from the combination of the relatively worse fit, blending constraint, and lower overall probability, leaving two surviving solutions with the planet/host mass ratios of $q\sim 2.8\times 10^{-5}$ and $\sim 1.1\times 10^{-5}$. A subtle central deviation supports the possibility of a tertiary lens component, either a binary companion to the host with a very large or small separation or a second planet lying near the Einstein ring, but it is difficult to claim a secure detection due to the marginal fit improvement, lack of consistency among different data sets, and difficulty in uniquely specifying the nature of the tertiary component. With the observables of the event, it is estimated that the masses of the planet and host are $\sim (6.9~M_\oplus, 0.75~M_\odot)$ according to one solution and $\sim (2.8~M_\oplus, 0.80~M_\odot)$ according to the other solution, indicating that the planet is a super Earth around a K-type star, regardless of the solution.

astro-ph.EP↗
arXiv2021

The Weingarten Calculus

This is a short introduction to Weingarten Calculus. Weingarten Calculus is a method to compute the joint moments of matrix variables distributed according to the Haar measure of compact groups.

math-ph↗
arXiv2021

Symmetric group characters of almost square shape

We give closed product formulas for the irreducible characters of the symmetric groups related to rectangular `almost square' Young diagrams $p \times(p+δ)$ for a fixed value of an integer $δ$ and an arbitrary integer $p$.

math.CO↗
arXiv2020

Random strict partitions and random shifted tableaux

We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (Law of Large Numbers and Central Limit Theorem) for their shapes, provided that the representation character ratios and their cumulants converge to zero at some prescribed speed. Our class of examples includes uniformly random shifted standard tableaux with prescribed shape as well as shifted tableaux generated by some natural combinatorial algorithms (such as shifted Robinson-Schensted-Knuth correspondence) applied to a random input.

math.CO↗
arXiv2019

Linear versus spin: representation theory of the symmetric groups

We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition $ξ$ with analogous normalized linear characters evaluated on the double partition $D(ξ)$. We also relate some natural filtration on the usual (linear) Kerov-Olshanski algebra of polynomial functions on the set of Young diagrams with its spin counterpart. Finally, we give a spin counterpart to Stanley formula for the characters of the symmetric groups.

math.CO↗
arXiv2018

A Spin Analogue of Kerov Polynomials

Kerov polynomials describe normalized irreducible characters of the symmetric groups in terms of the free cumulants associated with Young diagrams. We suggest well-suited counterparts of the Kerov polynomials in spin (or projective) representation settings. We show that spin analogues of irreducible characters are polynomials in even free cumulants associated with double diagrams of strict partitions. Moreover, we present a conjecture for the positivity of their coefficients.

math.CO↗
arXiv2017

Weingarten calculus via orthogonality relations: new applications

Weingarten calculus is a completely general and explicit method to compute the moments of the Haar measure on compact subgroups of matrix algebras. Particular cases of this calculus were initiated by theoretical physicists -- including Weingarten, after whom this calculus was coined by the first author, after investigating it systematically. Substantial progress was achieved subsequently by the second author and coworkers, based on representation theoretic and combinatorial techniques. All formulas of `Weingarten calculus' are in the spirit of Weingarten's seminal paper [W78]. However, modern proofs are very different from Weingarten's initial ideas. In this paper, we revisit Weingarten's initial proof and we illustrate its power by uncovering two new important applications: (i) a uniform bound on the Weingarten function, that subsumes existing uniform bounds, and is optimal up to a polynomial factor, and (ii) an extension of Weingarten calculus to symmetric spaces and conceptual proofs of identities established by the second author.

math.CO↗
arXiv2016

Polynomiality of shifted Plancherel averages and content evaluations

The shifted Plancherel measure is a natural probability measure on strict partitions. We prove a polynomiality property for the averages of the shifted Plancherel measure. As an application, we give alternative proofs of some content evaluation formulas, obtained by Han and Xiong very recently. Our main tool is factorial Schur $Q$-functions.

math.CO↗
arXiv2016

Multiparticle correlations in mesoscopic scattering: boson sampling, birthday paradox, and Hong-Ou-Mandel profiles

The interplay between single-particle interference and quantum indistinguishability leads to signature correlations in many-body scattering. We uncover these with a semiclassical calculation of the transmission probabilities through mesoscopic cavities for systems of non-interacting particles. For chaotic cavities we provide the universal form of the first two moments of the transmission probabilities over ensembles of random unitary matrices, including weak localization and dephasing effects. If the incoming many-body state consists of two macroscopically occupied wavepackets, their time delay drives a quantum-classical transition along a boundary determined by the bosonic birthday paradox. Mesoscopic chaotic scattering of Bose-Einstein condensates is then a realistic candidate to build a boson sampler and to observe the macroscopic Hong-Ou-Mandel effect.

quant-ph↗
arXiv2015

Moments of traces of circular beta-ensembles

Let $θ_1,\ldots,θ_n$ be random variables from Dyson's circular $β$-ensemble with probability density function $\operatorname {Const}\cdot\prod_{1\leq j 0$, we obtain some inequalities on $\mathbb{E}[p_μ(Z_n)\bar{p_ν(Z_n)}]$, where $Z_n=(e^{iθ_1},\ldots,e^{iθ_n})$ and $p_μ$ is the power-sum symmetric function for partition $μ$. When $β=2$, our inequalities recover an identity by Diaconis and Evans for Haar-invariant unitary matrices. Further, we have the following: $ \lim_{n\to\infty}\mathbb{E}[p_μ(Z_n)\bar{p_ν(Z_n)}]= δ_{μν}(\frac{2}β)^{l(μ)}z_μ$ for any $β>0$ and partitions $μ,ν$; $\lim_{m\to\infty}\mathbb{E}[|p_m(Z_n)|^2]=n$ for any $β>0$ and $n\geq2$, where $l(μ)$ is the length of $μ$ and $z_μ$ is explicit on $μ$. These results apply to the three important ensembles: COE ($β=1$), CUE ($β=2$) and CSE ($β=4$). We further examine the nonasymptotic behavior of $\mathbb{E}[|p_m(Z_n)|^2]$ for $β=1,4$. The central limit theorems of $\sum_{j=1}^ng(e^{iθ_j})$ are obtained when (i) $g(z)$ is a polynomial and $β>0$ is arbitrary, or (ii) $g(z)$ has a Fourier expansion and $β=1,4$. The main tool is the Jack function.

math.PR↗
arXiv2014

Averages of ratios of characteristic polynomials in circular beta-ensembles and super-Jack polynomials

We study the averages of ratios of characteristic polynomials over circular $β$-ensembles, where $β$ is a positive real number. Using Jack polynomial theory, we obtain three expressions for ratio averages. Two of them are given as sums of super-Jack polynomials and another one is given by a hyperdeterminant. As applications, we give dual relations for ratio averages between $β$ and $4/β$.

math.PR↗
arXiv2014

ABJ Fractional Brane from ABJM Wilson Loop

We present a new Fermi gas formalism for the ABJ matrix model. This formulation identifies the effect of the fractional M2-brane in the ABJ matrix model as that of a composite Wilson loop operator in the corresponding ABJM matrix model. Using this formalism, we study the phase part of the ABJ partition function numerically and find a simple expression for it. We further compute a few exact values of the partition function at some coupling constants. Fitting these exact values against the expected form of the grand potential, we can determine the grand potential with exact coefficients. The results at various coupling constants enable us to conjecture an explicit form of the grand potential for general coupling constants. The part of the conjectured grand potential from the perturbative sum, worldsheet instantons and bound states is regarded as a natural generalization of that in the ABJM matrix model, though the membrane instanton part contains a new contribution.

hep-th↗
arXiv2012

Moments of a single entry of circular orthogonal ensembles and Weingarten calculus

Consider a symmetric unitary random matrix $V=(v_{ij})_{1 \le i,j \le N}$ from a circular orthogonal ensemble. In this paper, we study moments of a single entry $v_{ij}$. For a diagonal entry $v_{ii}$ we give the explicit values of the moments, and for an off-diagonal entry $v_{ij}$ we give leading and subleading terms in the asymptotic expansion with respect to a large matrix size $N$. Our technique is to apply the Weingarten calculus for a Haar-distributed unitary matrix.

math.PR↗
arXiv2012

Integration of invariant matrices and application to statistics

We consider random matrices that have invariance properties under the action of unitary groups (either a left-right invariance, or a conjugacy invariance), and we give formulas for moments in terms of functions of eigenvalues. Our main tool is the Weingarten calculus. As an application to statistics, we obtain new formulas for the pseudo inverse of Gaussian matrices and for the inverse of compound Wishart matrices.

math.ST↗