Sato Ryosuke(Faculty of Science　Mathematics　Mathematics)

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Sato Ryosuke

Faculty of Science　Mathematics　Mathematics Assistant Professor

Researcher basic information

■ Degree

Ph.D. in Mathematical Science, Nagoya University, Mar. 2022

■ URL
researchmap URL

https://researchmap.jp/ryosuke_sato?lang=en

ホームページURL

https://jglobal.jst.go.jp/detail?JGLOBAL_ID=202501004625915013

■ Various IDs
J-Global ID

202501004625915013

■ Educational Organization

Bachelor's degree program, School of Science

Master's degree program, Graduate School of Science

Doctoral (PhD) degree program, Graduate School of Science

Career

■ Career
Career

Apr. 2025 - Present
Hokkaido University, Faculty of Science Department of Mathematics, Assistant Professor, Japan

Research activity information

■ Papers

Variations on quantum de Finetti theorems and operator valued Martin boundaries: A Choquet–Deny approach
Benoît Collins; Thierry Giordano; Ryosuke Sato
Proceedings of the American Mathematical Society, 154, 3, 1233, 1249, American Mathematical Society (AMS), 15 Jan. 2026, [Peer-reviewed]
Scientific journal,
We revisit the quantum de Finetti theorem. We state and prove a couple of variants thereof. In parallel, we introduce an operator version of the Martin boundary on quantum groups and prove generalizations of Biane’s theorem. Our proof of the de Finetti theorem is new in the sense that it is based on an analogy with the theory of operator-valued Martin boundary that we introduce.

GICAR Algebras and Dynamics on Determinantal Point Processes: Discrete Orthogonal Polynomial Ensemble Case
Ryosuke Sato
Communications in Mathematical Physics, 405, 5, Springer Science and Business Media LLC, 25 Apr. 2024, [Peer-reviewed]
Scientific journal

Multiplicative Characters and Gaussian Fluctuation Limits
Ryosuke Sato
Symmetry, Integrability and Geometry: Methods and Applications, SIGMA (Symmetry, Integrability and Geometry: Methods and Application), 03 Oct. 2023, [Peer-reviewed]
Scientific journal, It is known that extreme characters of several inductive limits of compact groups exhibit multiplicativity in a certain sense. In the paper, we formulate such multiplicativity for inductive limit quantum groups and provide explicit examples of multiplicative characters in the case of quantum unitary groups. Furthermore, we show a Gaussian fluctuation limit theorem using this concept of multiplicativity.

Characters of infinite-dimensional quantum classical groups: BCD cases
Ryosuke Sato
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 24, 04, World Scientific Pub Co Pte Ltd, 30 Dec. 2021, [Peer-reviewed]
Scientific journal, We study the character theory of inductive limits of [Formula: see text]-deformed classical compact groups. In particular, we clarify the relationship between the representation theory of Drinfeld–Jimbo quantized universal enveloping algebras and our previous work on the quantized characters. We also apply the character theory to construct Markov semigroups on unitary duals of [Formula: see text], [Formula: see text], and their inductive limits.

Inductive limits of compact quantum groups and their unitary representations
Ryosuke Sato
Letters in Mathematical Physics, 111, 5, Springer Science and Business Media LLC, 24 Sep. 2021, [Peer-reviewed]
Scientific journal

Quantized Vershik–Kerov theory and quantized central measures on branching graphs
Ryosuke Sato
Journal of Functional Analysis, 277, 8, 2522, 2557, Elsevier BV, Oct. 2019, [Peer-reviewed]
Scientific journal

Type classification of extreme quantized characters
RYOSUKE SATO
Ergodic Theory and Dynamical Systems, 41, 2, 593, 605, Cambridge University Press (CUP), 06 Sep. 2019, [Peer-reviewed]
Scientific journal, The notion of quantized characters was introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory forquantum groups. As in the case of ordinary groups, the representation associated with any extreme quantized character generates a von Neumann factor. From the viewpoint of operator algebras (and measurable dynamical systems), it is natural to ask what is the Murray–von Neumann–Connes type of the resulting factor. In this paper, we give a complete solution to this question when the inductive system is of quantum unitary groups $U_{q}(N)$.

■ Lectures, oral presentations, etc.

Conservation operator processes and their CLT from asymptotic representation theory
Rigorous Statistical Mechanics and Related Topics 2025, Nov. 2025

Conservation operator processes from asymptotic representation theory and their CLT
Ryosuke Sato
NCTS-AS Workshop on Free Probability Theory and Random Matrix Theory, Oct. 2025

Conservation operator processes from asymptotic representation theory and their CLT
Ryosuke Sato
Non-commutative Probability and Related Topics 2025, Oct. 2025

CAR algebras and stochastic dynamics on point processes
Ryosuke Sato
Mathematical aspects if quantum fields and related topics, May 2025

Operator-algebraic approach to stochastic processes on determinantal point processes
Ryosuke Sato
Non-commutative probability, random matrices and Lévy processes, Mar. 2025

The quantum de Finetti theorem and operator-valued Martin boundaries
Ryosuke Sato
作用素論・作用素環論研究集会, Nov. 2024

Dynamical relation between determinantal point processes and operator algebras
Ryosuke Sato
Rigorous Statistical Mechanics and Related Topics, Nov. 2024

Non-commutative random walks and the quantum de Finetti theorem
Ryosuke Sato
Non-commutative Probability and Related Topics 2024, Oct. 2024

CAR algebras and stochastic dynamics on random point processes
Ryosuke Sato
日本数学会2024年度秋季総合分科会, Sep. 2024

Stochastic dynamics on DPPs: From the viewpoint of operator algebras
Ryosuke Sato
無限粒子系、確率場の諸問題XVIII, Jan. 2024

Stochastic dynamics on DPPs and GICAR algebras
Ryosuke Sato
Random Interacting Systems, Scaling Limits, and Universality, Dec. 2023

On the interaction between determinantal point processes and operator algebras
Ryosuke Sato
Non-commutative Probability Theory, Random Matrix Theory and their Applications, Nov. 2023

Dynamics on DPPs and GICAR algebras
Ryosuke Sato
Non-Commutative Probability and Related Topics 2023, Oct. 2023

Stochastic dynamics on DPPs and GICAR algebras
Ryosuke Sato
The 21st Symposium Stochastic Analysis on Large Scale Interacting Systems, Oct. 2023

GICAR algebras and dynamics on determinantal point processes: orthogonal polynomial ensemble case
Ryosuke Sato
Recent Developments in Operator Algebras, Sep. 2023

Determinantal point processes and gauge-invariant CAR algebras
Ryosuke Sato
Random Matrices and Applications, Jun. 2023

Multiplicative characters and Gaussian fluctuation limits
Ryosuke Sato
Non-commutative Probability and Related Topics 2022, Nov. 2022

Markov processes on duals of quantum groups
Ryosuke Sato
Operator Algebras and Quantum Dynamical Systems, Feb. 2021

q-Schur generating functions and tensor porduct representations
Ryosuke Sato
作用素環の分類理論における新展開, Jan. 2020

Ergodic theoretical aspects of asymptotic representation theory
Ryosuke Sato
Nomcommutative probability and related fields, Nov. 2019

q-Schur generating functions and tensor product representations
Ryosuke Sato
Interactions between commutative and non-commutative probability, Aug. 2019

Asymptotic representation theory for quantum groups
Ryosuke Sato
Virginia Integrable Probability Summer School, Jun. 2019

Extremal quantized characters and biorthogonal ensembles
Ryosuke Sato
New Developments in Free Probability and Applications (Workshop2 : the applied perspective), Mar. 2019

Quantum group analogue of the Vershik-Kerov theory and the probability theory of the Gelfand-Tsetlin graph
Ryosuke Sato
Recent Developments in Operator Algebras, Sep. 2018

Quantized Vershik-Kerov theory and q-deformed Gelfand-Tsetlin graph
Ryosuke Sato
Random Matrices and their applications, May 2018

■ Affiliated academic society

Jun. 2024 - Present
The Mathematical Society of Japan

■ Research Themes

Algebraic integrable probability theory
Grants-in-Aid for Scientific Research
Apr. 2022 - Mar. 2025
佐藤僚亮
ランダム点過程を作用素環論の観点から研究した．特にランダム点過程のうち，その点同士の相関が行列式の形で表されるものを行列式点過程と呼び，ランダム行列理論や組合せ論，統計力学，表現論に関連する確率論などで研究されている．一方の作用素環論では，正準反交換関係を満たす生成元を持つCAR代数が様々な研究で重要な役割を果たしてきた．特に適当な設定の下で，CAR代数の状態は離散空間上のランダム点過程を与える．さらに状態がゲージ不変・準自由という性質を満たすとき，対応するランダム点過程は行列式点過程であることが，これまでの研究で知られていた．本研究では，この状態とランダム点過程との関係の発展を目指している．具体的には，作用素環論の立場から，ランダム点過程を不変測度とする確率過程を構成し，解析する理論を目指している．ここまでの業績として，ランダム点過程が直交多項式と関連する行列式点過程である場合，それを不変とするMarkov過程をCAR代数上の量子Markov半群から構成した．さらに構成したMarkov過程の推移確率と生成作用素の具体的な表示を与えた．この結果は論文にまとめ，Communication in Mathematical Physicsより出版された．またこの結果について研究会や研究セミナーなどで発表した．
別の話題の研究として，コンパクト群の双対空間上の量子Markov半群と量子情報理論との関係に関する共同研究も行なった．特に量子情報理論における基本的な定理である量子de Finetti定理について新たな観点と新しい証明を与えた．
Japan Society for the Promotion of Science, Grant-in-Aid for JSPS Fellows, Chuo University, 22KJ2770