Sakagawa, Hironobu

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics (Yagami)

Position

Professor
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Career 【 Display / hide 】

  • 2002.04
    -
    2007.03

    慶應義塾大学（理工学部），助手

  • 2004.09
    -
    2006.09

    日本学術振興会海外特別研究員(パリ第７大学）

  • 2007.04
    -
    2009.03

    慶應義塾大学（理工学部），助教

  • 2009.04
    -
    2014.03

    慶應義塾大学（理工学部），専任講師

  • 2014.04
    -
    Present

    慶應義塾大学（理工学部），准教授

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Academic Background 【 Display / hide 】

  • 1997.03

    Keio University, Faculty of Science and Engineering

    University, Graduated

  • 1999.03

    The University of Tokyo, Graduate School, Division of Mathematical Sciences

    Graduate School, Completed, Master's course

  • 2002.03

    The University of Tokyo, Graduate School, Division of Mathematical Sciences

    Graduate School, Completed, Doctoral course

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Academic Degrees 【 Display / hide 】

  • Ph.D., The University of Tokyo, 2002.03

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Research Areas 【 Display / hide 】

  • Natural Science / Basic mathematics (数学一般（含確率論・統計数学）)

  • Natural Science / Applied mathematics and statistics (数学一般（含確率論・統計数学）)

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Research Keywords 【 Display / hide 】

  • 相互作用系

  • 確率論

  • 統計力学

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Papers 【 Display / hide 】

  • Maximum of the Gaussian Interface Model in Random External Fields

    Sakagawa H.

    Journal of Statistical Physics 191 ( 8 )  2024.08

    ISSN  00224715

    　View Summary

    We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on RΛN, ΛN=[-N,N]d∩Zd with Hamiltonian HN(ϕ)=14d∑x∼y(ϕ(x)-ϕ(y))2-∑x∈ΛNη(x)ϕ(x) and 0-boundary conditions. {η(x)}x∈Zd is a family of i.i.d. symmetric random variables. We study how the typical maximal height of a random interface is modified by the addition of quenched bulk disorder. We show that the asymptotic behavior of the maximum changes depending on the tail behavior of the random variable η(x) when d≥5. In particular, we identify the leading order asymptotics of the maximum.

  • Behavior of the Lattice Gaussian Free Field with Weak Repulsive Potentials

    Sakagawa H.

    Journal of Statistical Physics (Journal of Statistical Physics)  182 ( 1 )  2021.01

    ISSN  00224715

    　View Summary

    We consider the d(≥3) - dimensional lattice Gaussian free field on Λ : = [- N, N] ∩ Z in the presence of a self-potential of the form U(r) = - bI(| r| ≤ a) , a> 0 , b∈ R. When b> 0 , the potential attracts the field to the level around zero and is called square-well pinning. It is known that the field turns to be localized and massive for every a> 0 and b> 0. In this paper, we consider the situation that the parameter b< 0 and self-potentials are imposed on ΛαN,α∈(0,1). We prove that once we impose this weak repulsive potential from the level [- a, a] , most sites are located on the same side and the field is pushed to the same level when the original Gaussian field is conditioned to be positive everywhere, or negative everywhere with probability 12, respectively. This result can be applied to show the similar path behavior for the disordered pinning model in the delocalized regime. N d d

  • Localization of a Gaussian membrane model with weak pinning potentials

    坂川 博宣

    ALEA Lat. Am. J. Probab. Math. Stat. (Alea)  15 ( 2 ) 1123 - 1140 2018

    Research paper (scientific journal), Single Work, Accepted,  ISSN  19800436

    　View Summary

    © 2019 ALEA, Lat. Am. J. Probab. Math. Stat. We consider a class of effective models on ℤd called Gaussian membrane models with square-well pinning or σ-pinning. It is known that when d = 1 this model exhibits a localization/delocalization transition that depends on the strength of the pinning. In this paper, we show that when d ≥ 2, once we impose weak pinning potentials the field is always localized in the sense that the corresponding free energy is always positive. We also discuss the case that both square-well potentials and repulsive potentials are acting in high dimensions.

  • On the probability that Laplacian interface models stay positive in subcritical dimensions

    SAKAGAWA HIRONOBU

    RIMS Kôkyûroku Bessatsu B59   273 - 288 2016

    Research paper (conference, symposium, etc.), Single Work, Accepted

  • Persistence probability for a class of Gaussian processes related to random interface models

    SAKAGAWA HIRONOBU

    Adv. in Appl. Probab. 47 ( 1 ) 146 - 163 2015

    Research paper (scientific journal), Single Work, Accepted

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Presentations 【 Display / hide 】

  • Behavior of the lattice Gaussian free field with weak repulsive potentials

    坂川博宣

    無限粒子系、確率場の諸問題XV, 

    2020.01
    , 

    Oral presentation (general)

  • 離散Gauss自由場に対するレベル集合パーコレーションについて

    坂川博宣

    確率論サマースクール, 

    2018.08
    , 

    Oral presentation (invited, special)

  • Gauss膜モデルの漸近挙動について

    坂川博宣

    確率論サマースクール, 

    2018.08
    , 

    Oral presentation (invited, special)

  • Localization of the Gaussian membrane model with weak pinning potentials

    坂川博宣

    Topics in Probability Theory, 

    2018.03
    , 

    Oral presentation (general)

  • Localization of the Gaussian membrane model with weak pinning potentials

    坂川博宣

    無限粒子系、確率場の諸問題XII, 

    2017.01
    , 

    Oral presentation (general)

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • 相分離界面に関連した確率場の漸近挙動の研究

    2022.04
    -
    2025.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 基盤研究(C), Principal investigator

  • Study on random fields with long range correlations related to phase separating interfaces

    2014.04
    -
    2017.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

    　View Summary

    In this research, we studied several random fields with long range correlations for mathematical analysis of phase separating interfaces and membranes. In particular, we considered the Δφ interface model and obtained the following results:
    (1) We give an estimate on the probability that the field stays positive in low dimensions and its behaviors differ greatly from those of the higher dimensional case or other random interface models.(2) We show that in the case of two or more dimensions, once we impose weak pinning potentials the field is always localized in the sense that the corresponding free energy is always positive.

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Courses Taught 【 Display / hide 】

  • PRINCIPLES OF PROBABILITY THEORY

    2024

  • MATHEMATICS 1B

    2024

  • MATHEMATICS 1A

    2024

  • LINEAR ALGEBRA

    2024

  • INDEPENDENT STUDY ON FUNDAMENTAL SCIENCE AND TECHNOLOGY

    2024

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Memberships in Academic Societies 【 Display / hide 】

  • 日本数学会, 

    2003.04
    -
    Present
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