2022/01/24 更新

写真a

フナキ タダヒサ
舟木 直久
所属
理工学術院 基幹理工学部
職名
特任教授

学内研究所等

  • 2020年
    -
    2022年

    理工学術院総合研究所   兼任研究員

学位

  • 理学博士

経歴

  •  
     
     

    東京大学 大学院数理科学研究科 基礎解析学   教授

所属学協会

  •  
     
     

    日本数学会

 

研究分野

  • 基礎解析学

  • 応用数学、統計数学

  • 数学基礎

研究キーワード

  • 確率論

  • Probability Theory

書籍等出版物

  • Lectures on Probability Theory and Statistics, Ecole d'Et\'e de Probabilit\'es de Saint-Flour XXXIII - 2003 (共著)

    Lect. Notes Math., 1869, Springer  2005年

  • Lectures on probability theory and statistics. Lectures from the 33rd Probability Summer School held in Saint-Flour, July 6-23, 2003 (with A. Dembo)

    Lecture Notes in Math., 1869, Springer  2005年

  • 確率論

    朝倉書店  2004年

  • Stochastic Analysis on Large Scale Interacting Systems (2002), the Proceedings of Shonan/Kyoto meetings. (edior)

    Advanced Studies in Pure Mathematics, 39, 日本数学会  2004年

  • Probability Theory (Japanese)

    Asakura, viii+263 pages  2004年

  • Stochastic Analysis on Large Scale Interacting Systems (Proceedings of Shonan/Kyoto meetings 2002, editor)

    Adv. Stud. Pure Math., 39, Math. Soc. Japan  2004年

  • ミクロからマクロへ, 2.格子気体の流体力学極限(共著)

    シュプリンガー・フェアラーク東京  2002年

  • ミクロからマクロへ,1. 界面モデルの数理(共著)

    シュプリンガー・フェアラーク東京  2002年

  • From Micro to Macro 2, Hydrodynamic Limit for Lattice Gas (Japanese, with K. Uchiyama)

    Springer Tokyo, xvi+304 pages  2002年

  • From Micro to Macro 1, Mathematical Theory of Interface Models (Japanese, with K. Uchiyama)

    Springer Tokyo, xii+284 pages  2002年

  • 確率微分方程式

    岩波書店  1997年

     概要を見る

    1997, 2005

  • Stochastic Differential Equation (Japanese)

    Iwanami, xviii+187 pages  1997年

     概要を見る

    1997, 2005

  • Nonlinear Stochastic PDEs: Hydrodynamic Limit and Burgers' Turbulence. (editor)

    IMA volumes in Mathematics and its Applications, 77, Univ. Minnesota, Springer  1995年

  • Nonlinear Stochastic PDE's : Hydrodynamic Limit and Burger's Turbulence (editor)

    IMA volumes in Mathematics and its Applications  1995年

▼全件表示

Misc

  • Concentration under scaling limits for weakly pinned Gaussian random walks

    Erwin Bolthausen, Tadahisa Funaki, Tatsushi Otobe

    PROBABILITY THEORY AND RELATED FIELDS   143 ( 3-4 ) 441 - 480  2009年03月

     概要を見る

    We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of R(d), especially under the critical situation that the rate functional of the corresponding large deviation principle admits two minimizers. We obtain different type of limits, in a positive recurrent regime, depending on the co-dimension of the subspace and the conditions imposed at the final time under the presence or absence of a wall. The motivation comes from the study of polymers or (1 + 1)-dimensional interfaces with delta-pinning.

    DOI CiNii

  • A stochastic heat equation with the distributions of Levy processes as its invariant measures

    Tadahisa Funaki, Bin Xie

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS   119 ( 2 ) 307 - 326  2009年02月

     概要を見る

    We consider a linear heat equation on a half line with an additive noise chosen properly ill Such a manner that its invariant Measures are a class of distributions of Levy processes. Our assumption oil the corresponding Levy measure is, in general, mild except that we need its integrability to show that the distributions of Levy processes are the only invariant measures of the stochastic heat equation. (C) 2009 Elsevier B.V. All rights reserved.

    DOI

  • Stochastic analysis on large scale interacting systems

    Selected Papers on Probability and Statistics, Translations, Series 2, Amer. Math. Soc.   227   49 - 73  2009年

  • A scaling limit for weakly pinned Gaussian random walks

    RIMS Kokyuroku Bessatsu   B6   97 - 109  2008年

  • Stochastic analysis on large scale interacting systems (Japanese)

    Sugaku   60 ( 2 ) 113 - 133  2008年

  • Dichotomy in a scaling limit under Wiener measure with density

    Tadahisa Funaki

    ELECTRONIC COMMUNICATIONS IN PROBABILITY   12   173 - 183  2007年05月

     概要を見る

    In general, if the large deviation principle holds for a sequence of probability measures and its rate functional admits a unique minimizer, then the measures asymptotically concentrate in its neighborhood so that the law of large numbers follows. This paper discusses the situation that the rate functional has two distinct minimizers, for a simple model described by the pinned Wiener measures with certain densities involving a scaling. We study their asymptotic behavior and determine to which minimizers they converge based on a more precise investigation than the large deviation's level.

  • Integration by parts formulae for Wiener measures on a path space between two curves

    Tadahisa Funaki, Kensuke Ishitani

    PROBABILITY THEORY AND RELATED FIELDS   137 ( 3-4 ) 289 - 321  2007年03月

     概要を見る

    This paper is concerned with the integration by parts formulae for the pinned or the standard Wiener measures restricted on a space of paths staying between two curves. The boundary measures, concentrated on the set of paths touching one of the curves once, are specified. Our approach is based on the polygonal approximations. In particular, to establish the convergence of boundary terms, a uniform estimate is derived by means of comparison argument for a sequence of random walks conditioned to stay between two polygons. Applying the Brascamp-Lieb inequality, the stochastic integrals of Wiener type are constructed relative to the three-dimensional Bessel bridge or the Brownian meander.

    DOI

  • Dynamic approach to a stochastic domination: The FKG and Brascamp-Lieb inequalities (with K. Toukairin)

    Proc. Amer. Math. Soc.   135 ( 6 ) 1915 - 1922  2007年

    DOI

  • Hydrodynamic limit and nonlinear PDEs with singularities

    Proceedings of MSJ-IRI meeting "Asymptotic Analysis and Singularities -- elliptic and parabolic PDEs and related problems" (2005), Adv. Stud. Pure Math., Math. Soc. Japan   47 ( 2 ) 421 - 440  2007年

  • On some Fourier aspects of the construction of certain Wiener integrals (with Y. Hariya, F. Hirsch, M. Yor)

    Stochastic Process. Appl.   117 ( 1 ) 1 - 22  2007年

  • Wiener integrals for centered powers of Bessel processes, I. (with Y. Hariya, M. Yor)

    Markov Process. Related Fields   13 ( 1 ) 21 - 56  2007年

  • On the construction of Wiener integrals with respect to certain pseudo-Bessel processes (with Y. Hariya, F. Hirsch, M. Yor)

    Stochastic Process. Appl.   116 ( 12 ) 1690 - 1711  2006年

  • Wiener integrals for centered Bessel and related processes, II (with Y. Hariya, M. Yor)

    ALEA (Lat. Am. J. Probabi. Math. Stat.)   1   225 - 240  2006年

  • Stochastic Interface Models

    Lecture Notes in Math., Springer   1869   103 - 274  2005年

  • Zero temperature limit for interacting Brownian particles. I. Motion of a single body

    T Funaki

    ANNALS OF PROBABILITY   32 ( 2 ) 1201 - 1227  2004年04月

     概要を見る

    We consider a system of interacting Brownian particles in R-d with a pairwise potential, which is radially symmetric, of finite range and attains a unique minimum when the distance of two particles becomes a > 0. The asymptotic behavior of the system is studied under the zero temperature limit from both microscopic and macroscopic aspects. If the system is rigidly crystallized, namely if the particles are rigidly arranged in an equal distance a, the crystallization is kept under the evolution in macroscopic time scale. Then, assuming that the crystal has a definite limit shape under a macroscopic spatial scaling, the translational and rotational motions of such shape are characterized.

    DOI

  • Zero temperature limit for interacting Brownian particles. II. Coagulation in one dimension

    T Funaki

    ANNALS OF PROBABILITY   32 ( 2 ) 1228 - 1246  2004年04月

     概要を見る

    We study the zero temperature limit for interacting Brownian particles in one dimension with a pairwise potential which is of finite range and attains a unique minimum when the distance of two particles becomes a > 0. We say a chain is formed when the particles are arranged in an "almost equal" distance a. If a chain is formed at time 0, so is for positive time as the temperature of the system decreases to 0 and, under a suitable macroscopic space-time scaling, the center of mass of the chain performs the Brownian motion with the speed inversely proportional to the total mass. If there are two chains, they independently move until the time when they meet. Then, they immediately coalesce and continue the evolution as a single chain. This can be extended for finitely many chains.

    DOI

  • Large deviations for ∇φ interface model and derivation of free boundary problems (with H. Sakagawa)

    Proceedings of Shonan/Kyoto meetings; Stochastic Analysis on Large Scale Interacting Systems(2002), Adv. Stud. Pure Math., Math. Soc. Japan   39   173 - 211  2004年

  • Hydrodynamic limit for del phi interface model on a wall

    T Funaki

    PROBABILITY THEORY AND RELATED FIELDS   126 ( 2 ) 155 - 183  2003年

     概要を見る

    We consider random evolution of an interface on a hard wall under periodic boundary conditions. The dynamics are governed by a system of stochastic differential equations of Skorohod type, which is Langevin equation associated with massless Hamiltonian added a strong repelling force for the interface to stay over the wall. We study its macroscopic behavior under a suitable large scale space-time limit and derive a nonlinear partial differential equation, which describes the mean curvature motion except for some anisotropy effects, with reflection at the wall. Such equation is characterized by an evolutionary variational inequality.

    DOI

  • Stochastic models for phase separation and evolution equations of interfaces

    Sugaku Expositions   16 ( 1 ) 97 - 116  2003年

  • Large deviations for the Ginzburg-Landau ∇φ interface model (with T. Nishikawa)

    Probab. Theory Related Fields   120 ( 4 ) 538 - 568  2001年

  • Fluctuations for ∇φ interface model on a wall (with S. Olla)

    Stochastic Process. Appl.   94 ( 1 ) 1 - 27  2001年

  • Recent results on the Ginzburg-Landan ∇φ interface model

    Hydrodynamic Limits and Related Topics, Fields Inst. Commun., Amer. Math. Soc.   27   71 - 81  2000年

  • Free boundary problem from stochastic lattice gas model

    T Funaki

    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES   35 ( 5 ) 573 - 603  1999年09月

     概要を見る

    We consider a system consisting of two types of particles called "water" and "ice" on d-dimensional periodic lattices. The water particles perform excluded interacting random walks (stochastic lattice gases), while the ice particles are immobile, When a water particle touches an ice particle, it immediately dies. On the other hand, the ice particle disappears after receiving the lth visit from water particles. This interaction models the melting of a solid with latent heat, We derive the nonlinear one-phase Stefan free boundary problem in a hydrodynamic scaling limit. Derivation of two-phase Stefan problem is also discussed. (C) Elsevier, Paris.

  • Interacting particle approximation for nonlocal quadratic evolution problems (with P. Biler, W.A. Woyczynski)

    Probab. Math. Statist.   19 ( 2 ) 267 - 286  1999年

  • Singular limit for stochastic reaction-diffusion equation and generation of random interfaces

    Acta Math. Sin. (Engl. Ser.)   15 ( 3 ) 407 - 438  1999年

  • Interacting particle approximation for fractal Burgers equation (with W.A. Woyczynski)

    Stochastic Processes and Related Topics, In Memory of Stamatis Cambanis 1943-1995, Trends Math.     141 - 166  1998年

  • Fractal Burgers equations (with P. Biler, W.A. Woyczynski)

    J. Differential Equations   148 ( 1 ) 9 - 46  1998年

  • Probability models for phase separation and the equations of motion for interfaces (Japanese)

    Sugaku   50 ( 1 ) 68 - 85  1998年

  • Singular limit for reaction-diffusion equation with self-similar Gaussian noise

    T Funaki

    NEW TRENDS IN STOCHASTIC ANALYSIS     132 - 152  1997年

     概要を見る

    Singular limit is investigated for 1-dimensional bistable reaction-diffusion equations added a self-similar Gaussian noise. The solution converges to one of the stable phases determined from the reaction term and accordingly a phase separation is formed in the Limit. We shall derive a stochastic differential equation which describes the dynamics of the phase separation point. This is a continuation and generalization of the former paper [12].

  • Motion by mean curvature from the Ginzburg-Landau ∇φ interface model (with H. Spohn)

    Comm. Math. Phys.   185 ( 1 ) 1 - 36  1997年

    DOI CiNii

  • Equilibrium fluctuations for lattice gas

    It^o's stochastic calculus and probability theory, Springer     63 - 72  1996年

  • Hydrodynamic limit for lattice gas reversible under Bernoulli measures (with K. Uchiyama, H.T. Yau)

    Nonlinear Stochastic PDEs (Minneapolis, 1994) IMA Vol. Math. Appl., Springer   77   1 - 40  1996年

  • THE SCALING LIMIT FOR A STOCHASTIC PDE AND THE SEPARATION OF PHASES

    T FUNAKI

    PROBABILITY THEORY AND RELATED FIELDS   102 ( 2 ) 221 - 288  1995年06月

     概要を見る

    We investigate the problem of singular perturbation for a reaction-diffusion equation with additive noise (or a stochastic partial differential equation of Ginzburg-Landau type) under the situation that the reaction term is determined by a potential with double-wells of equal depth. As the parameter epsilon (the temperature of the system) tends to 0, the solution converges to one of the two stable phases and consequently the phase separation is formed in the limit. We derive a stochastic differential equation which describes the random movement of the phase separation point. The proof consists of two main steps. We show that the solution stays near a manifold M(epsilon) of minimal energy configurations based on a Lyapunov type argument. Then, the limit equation is identified by introducing a nice coordinate system in a neighborhood of M(epsilon).

  • Gibbs-Cox random fields and Burgers' turbulence (with D. Surgailis, W.A. Woyczynski)

    Ann. Appl. Probab.   5 ( 2 ) 461 - 492  1995年

  • Low temperature limit and separation of phases for Ginzburg-Landau stochastic equation

    Stochastic analysis on infinite-dimensional spaces (Baton Rouge, 1994), Pitman Res. Notes Math. Ser.   310   88 - 98  1994年

  • Stationary states of random Hamiltonian systems (with J. Fritz, J.L. Lebowitz)

    Probab. Theory Related Fields   99 ( 2 ) 211 - 236  1994年

  • Degenerative convergence of diffusion process toward a submanifold by strong drift (with H. Nagai)

    Stochastics Stochastics Rep.   44 ( 1-2 ) 1 - 25  1993年

  • A STOCHASTIC PARTIAL-DIFFERENTIAL EQUATION WITH VALUES IN A MANIFOLD

    T FUNAKI

    JOURNAL OF FUNCTIONAL ANALYSIS   109 ( 2 ) 257 - 288  1992年11月

  • On the stochastic partial differential equations of Ginzbung-Landan type

    Lecture Notes in Control and Inform. Sci., Springer   176   113 - 122  1992年

  • THE REVERSIBLE MEASURES OF MULTIDIMENSIONAL GINZBURG-LANDAU TYPE CONTINUUM MODEL

    T FUNAKI

    OSAKA JOURNAL OF MATHEMATICS   28 ( 3 ) 463 - 494  1991年09月

  • REGULARITY PROPERTIES FOR STOCHASTIC PARTIAL-DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE

    T FUNAKI

    OSAKA JOURNAL OF MATHEMATICS   28 ( 3 ) 495 - 516  1991年09月

  • THE HYDRODYNAMIC LIMIT FOR A SYSTEM WITH INTERACTIONS PRESCRIBED BY GINZBURG-LANDAU TYPE RANDOM HAMILTONIAN

    T FUNAKI

    PROBABILITY THEORY AND RELATED FIELDS   90 ( 4 ) 519 - 562  1991年

     概要を見る

    As a microscopic model we consider a system of interacting continuum like spin field over R(d). Its evolution law is determined by the Ginzburg-Landau type random Hamiltonian and the total spin of the system is preserved by this evolution. We show that the spin field converges, under the hydrodynamic space-time scaling, to a deterministic limit which is a solution of a certain nonlinear diffusion equation. This equation describes the time evolution of the macroscopic field. The hydrodynamic scaling has an effect of the homogenization on the system at the same time.

  • Hydrodynamic limit of one-dimensional exclusion processes with speed change (with K. Handa, K. Uchiyama)

    Ann. Probab.   19 ( 1 ) 245 - 265  1991年

  • Hydrodynamic limit for Ginzburg-Landau type continuum model

    Probability theory and mathematical statistics (Vilnius, 1989)   I   382 - 390  1990年

  • DERIVATION OF THE HYDRODYNAMICAL EQUATION FOR ONE-DIMENSIONAL GINZBURG-LANDAU MODEL

    T FUNAKI

    PROBABILITY THEORY AND RELATED FIELDS   82 ( 1 ) 39 - 93  1989年

  • THE HYDRODYNAMICAL LIMIT FOR SCALAR GINZBURG-LANDAU MODEL ON R

    T FUNAKI

    LECTURE NOTES IN MATHEMATICS   1322   28 - 36  1988年

  • ON DIFFUSIVE MOTION OF CLOSED CURVES

    T FUNAKI

    LECTURE NOTES IN MATHEMATICS   1299   86 - 94  1988年

  • The central limit theorem for the spatially homogeneous Boltzmann equation

    Probabilistic Methods in Mathematical Physics (Katata/Kyoto, 1985), Academic Press     91 - 111  1987年

  • CONSTRUCTION OF STOCHASTIC-PROCESSES ASSOCIATED WITH THE BOLTZMANN-EQUATION AND ITS APPLICATIONS

    T FUNAKI

    LECTURE NOTES IN MATHEMATICS   1203   51 - 65  1986年

  • THE DIFFUSION-APPROXIMATION OF THE SPATIALLY HOMOGENEOUS BOLTZMANN-EQUATION

    T FUNAKI

    DUKE MATHEMATICAL JOURNAL   52 ( 1 ) 1 - 23  1985年

  • Random Motion of Strings and Stochastic Differential Equations on the Space C([0, 1], Rd)

    Tadahisa Funaki

    North-Holland Mathematical Library   32 ( C ) 121 - 133  1984年01月

    DOI

  • A CERTAIN CLASS OF DIFFUSION-PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS

    T FUNAKI

    ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE   67 ( 3 ) 331 - 348  1984年

  • The diffusion approximation of the Boltzmann equation of Maxwellian molecules

    Publ. Res. Inst. Math. Sci.   19 ( 2 ) 841 - 886  1983年

  • RANDOM MOTION OF STRINGS AND RELATED STOCHASTIC-EVOLUTION EQUATIONS

    T FUNAKI

    NAGOYA MATHEMATICAL JOURNAL   89 ( MAR ) 129 - 193  1983年

  • Probabilistic construction of the solution of some higher order parabolic differenctial equation

    Proc. Japan Acad. Ser. A Math. Sci.   55 ( 5 ) 176 - 179  1979年

  • On a new derivation of the Navier-Stokes equation (with A. Inoue)

    Comm. Math. Phys.   65 ( 1 ) 83 - 90  1979年

    DOI CiNii

  • Construction of a solution of random transport equation with boundary condition

    J. Math. Soc. Japan   31 ( 4 ) 719 - 744  1979年

  • Probabilistic construction of the solution of some higher order parabolic differenctial equation

    Proc. Japan Acad. Ser. A Math. Sci.   55 ( 5 ) 176 - 179  1979年

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Works(作品等)

  • 第11回日本数学会国際研究集会(Mathematical Society of Japan - International Research Institute)「大規模相互作用系に関する確率解析 (Stochastic Analysis on Large Scale Interacting Systems)」組織委員長, 湘南国際村センター

    2002年
    -
     

受賞

  • 日本数学会賞秋季賞

    2007年  

  • 日本数学会解析学賞

    2002年  

共同研究・競争的資金等の研究課題

  • 確率偏微分方程式

  • 流体力学極限

  • 大規模相互作用系の確率解析

  • Stochastic partial differential equations

  • Hydrodynamic limit

  • Stochastic analysis on large scale interacting systems

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現在担当している科目

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