Research Papers

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  1. (with T. Mine) The transition operator of a random walk perturbated by sparse potentials. (submitted) ArXiv 2403.07345 pdf
  2. (with R. Fukushima, M. Nakashima) The period group of a characteristic function. Real Analysis Exchange 47 no 2 (2022), 323-332. DOI:10.14321/realanalexch.47.2.1633525535 pdf
  3. (with F. Comets, R. Fukushima, S. Nakajima) Limiting Results for the Free Energy of Directed Polymers in Random Environment with Unbounded Jumps J. Stat. Phys. Volume 161, Issue 3, (2015), pp 577-597 DOI:10.1007/s10955-015-1347-1 pdf.
  4. (with F. Comets) Localization Transition for Polymers in Poissonian Medium. Commun. Math. Phys. Vol 323, Issue 1 (2013) 417--447, DOI:10.1007/s00220-013-1744-8 pdf
  5. (with R. Fukushima) On the exponential growth for a certain class of linear systems. ALEA Lat. Am. J. of Prob. Math. Stat., 9 (2012), 323--336. pdf
  6. Stochastic Shear Thickening Fluids: Strong Convergence of the Galerkin Approximation and the Energy Equality. Ann. Appl. Probab., 2012, Vol. 22, No.3, 1215--1242. DOI:10.1214/11-AAP794 pdf
  7. (with Y. Terasawa) Stochastic Power Law Fluids: Existence and Uniqueness of Weak Solutions. Ann. Appl. Probab., Vol. 21, No 5 (2011), 1827--1859. DOI:10.1214/10-AAP741 pdf
  8. (with H. Heil, M. Nakashima) Branching Random Walks in Random Environment are Diffusive in the Regular Growth Phase, Electron. J. Probab. , Volume 16, (2011), 323--336. DOI: 10.1214/EJP.v16-922 pdf
  9. (with Y. Nagahata) A Note on the Diffusive Scaling Limit for a Class of Linear Systems,
    Electron. Commun. Probab. 15 (2010), 68--78. DOI: 10.1214/ECP.v15-1530 pdf
  10. (with Y. Nagahata) Localization for a Class of Linear Systems,
    Electron. J. Probab. Vol. 15, No. 20, (2010), 636--653. DOI: 10.1214/EJP.v15-757 pdf
  11. (with F. Comets) Branching Random Walks in Time-Space Random Environment: Survival Probability, Global and Local Growth Rates, J. Theoret. Probab. DOI:Volume 24, Number 3, 657-687 10.1007/s10959-009-0267-x pdf
  12. Localization for Linear Stochastic Evolutions,
    J. Stat. Phys. 138 , No.4/5, 598--618, (2010). DOI:10.1007/s10955-009-9876-0 pdf (with corrections to some small, harmless errors)
  13. (with Y. Nagahata) Central Limit Theorem for a Class of Linear Systems,
    Electron. J. Probab. Vol. 14, No. 34, 960--977. (2009). pdf
  14. (with Y. Hu) Localization for Branching Random Walks in Random Environment,
    Stoch. Proc. Appl. , Vol. 119, Issue 5, 1632--1651, (2009). pdf
  15. Phase Transitions for the Growth Rate of Linear Stochastic Evolutions,
    preprint, 2008, J. Stat. Phys. , 133 , No.6, 1033--1058, (2008). pdf
  16. Central Limit Theorem for Branching Random Walk in Random Environment,
    Ann. Appl. Probab., Vol. 18, No. 4, 1619--1635, 2008. pdf
  17. (with F. Comets) Directed Polymers in Random Environment are Diffusive at Weak Disorder,
    Ann. Probab. Vol. 34, No. 5, 1746--1770, 2006.
    ps.gz / pdf/
  18. (with F. Comets) Brownian directed polymers in random environment,
    Commun. Math. Phys. 54 , 257--287, no. 2. (2005).
    ps.gz/ pdf
  19. (with F. Comets) Some new results on Brownian directed polymers in random environment,
    RIMS Kokyuroku 1386 , 50--66, (2004).
    ps.gz / pdf/
  20. (with F. Comets and T. Shiga) Probabilistic analysis of directed polymers in random environment: a review,
    n Advanced Studies in Pure Mathematics 39 115---142, (2004)
    ps.gz / pdf
  21. Phase transition from the viewpoint of relaxation phenomena,
    Review in Mathematical Pysics Vol.15, No. 7 (2003) 765--788.
    ps.gz
  22. (with F. Comets and T. Shiga) Directed polymers in random environment: path localization and strong disorder,
    Bernoulli , 9 (3), 705--723, (2003).
    Preview the abstract. / dvi / ps.gz /pdf
  23. (with H. Tanemura) Localization transition of d-friendly walkers,
    Probab. Th. Rel. Fields , 125, 593 --608, (2003).
    Preview the abstract. / Preview the label. / pdf
  24. (with Y. Isozaki) Weakly pinned random walk on the wall: pathwise descriptions of the phase transition,
    Stoch. Proc. Appl. 96, 261 --284,(2001).
    Preview the abstract. / Download the dvi file
  25. (with K. S. Alexander) The spectral gap of 2-D stochastic Ising models with mixed boundary conditions,
    J. Stat. Phys. 104,, Nos. 1/2, 89--109, (2001).
    Preview the abstract. / Download the dvi file
  26. The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice,
    Ann. Inst. Henri Poincar\'e. Probabilit\'es et Statistiques 37, 2, 223--243 (2001)
    Preview the abstract. / Download the dvi file
  27. Application of log-Sobolev inequality to the stochastic dynamics of unbounded spin systems on the lattice,
    J. Funct. Anal. 173 , 74--102, (2000).
    Preview the abstract. / Download the dvi file
  28. The log-Sobolev inequality for weakly coupled lattice field,
    Probab. Th. Rel. Fields , 115 , 1--40, (1999).
    Preview the abstract.
    Download the dvi file
  29. Finite volume Glauber dynamics in a small magnetic field,
    J. Stat. Phys. 90 , Nos.3/4, (1998).
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  30. Exponential relaxation of finite volume Glauber dynamics near the border of the one phase region,
    in Trends in Probability and Related Analysis, the proceedings of SAP'96, ed. by N. Kono and N.-R. Shieh, World Scientific, 339--350, (1997).
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  31. Relaxed criteria of the Dobrushin-Shlosman mixing condition,
    J. Stat. Phys. 87, Nos.1/2, 293--309, (1997).
    Preview the abstract/ Download the dvi file
  32. (with Schonmann, R.) Exponential relaxation of Glauber dynamics with some special boundary conditions,
    Commun. Math. Phys. 189, 299--310, (1997).
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  33. (with Higuchi, Y.) Slow relaxation of 2-D stochastic Ising models with random and non-random boundary conditions,
    In: New trends in stochastic analysis, ed. by K. D. Elworthy, S. Kusuoka, I. Shigekawa, World Scientific Publishing, 153--167, (1997).
    Preview the abstract/ Download the dvi file
  34. (with Higuchi,Y.)Ising model on the lattice Sierpinski Gasket,
    J. Stat. Phys. , 84, Nos. 1/2 pp. 295--307, (1996).
    Preview the abstract/ Download the dvi file
  35. The Littlewood-Paley-Stein inequality on an infinite dimensional manifold,
    J. Funct. Anal. . 122, 402--427, (1994).
  36. A large deviation principle for (r,p)-capacities on the Wiener space,
    Probab. Th. Rel. Fields , 94, 473--488, (1993).
    Preview the abstract
  37. (with Shigekawa, I.) Littlewood-Paley-Stein inequality for symmetric diffusions,
    J. math. Soc. Japan, 44, pp.251-280 (1992).
  38. Sobolev spaces on a Riemannian manifold and their equivalence,
    J. Math. Kyoto Univ. 33 621--654,(1992).
    Preview the abstract

Lecture Notes

  1. 「ランダム媒質中のディレクティドポリマー」 数学 第 56 巻 第2号 2004 年 4 月 春期号 159--181 頁 pdf
  2. 「相転移と緩和現象」(サマースクール 数理物理 2001 での予稿） dvi
  3. A Course in Probability,
  4. (with Higuchi,Y.)Analytic conditions and phase transition for Ising models, (in Japanese) In: Seminar on Probability Vol. 58, 1--46, (1995). dvi

Selected Talks

  1. The transition operator of a random walk perturbated by sparse potentials. ( 大規模相互作用系の確率解析, November 18, 2024 at University of Tokyo). slides.
  2. "Survival rate for a random walks in disatrous environment'' ( Niigata Probability Workshop , January 21, 2016, Niigata University)
  3. "Survival rate for a certain class of random walks in random obstacles'' (The 13th Workshop pn Stochaastic Analysis on Large Scale Interacting Systems, November 5, 2014, University of Tokyo)
  4. Brownian Directed Polymers in Random Environment: Complete Localization and Phase Diagram. ( "Markov chain on graphs and related topics" February 13, 2013, RIMS, Kyoto).
  5. Brownian Directed Polymers in Random Environment: Complete Localization and Phase Diagram. ( ``Workshop on Random Polymers'', January 18, 2013, EURANDOM, Eindhoven).
  6. Brownian Directed Polymers in Random Environment: Complete Localization and Phase Diagram. ( ``Random media II'', September 5, 2012, WPI-AIMR, Main building, Tohoku University).
  7. Introduction to Stochastic Navier-Stokes equations I,II. 「偏微分方程式の背後にある確率課程と解の族が示す 統計力学的な現象の解析」December 19, 2011 at RIMS, Kyoto University.
  8. Linear Stochastic Growth Models, (Applications of RG Methods in Mathematical Sciences , September 14, 2011 at RIMS, Kyoto University.)
  9. Stochastic Power Law Fluids, ( PDE実解析研究会, April 20, 2011, at Univ. of Tokyo).
  10. Stochastic Power Law Fluids, ( Seminaire de Probabilite, March 22, 2011, at Uviversite Paris Diderot --Paris 7).
  11. Stochastic Shear Thickening Fluids: Strong Convergence of the Garelkin Approximation and the Energy Equality. (CREST Seminar, February 4, 2011, Tohoku University) notes.
  12. Stochastic Shear Thickening Fluids: Strong Convergence of the Garelkin Approximation and the Energy Equality. (Probability Seminar, June 7, 2010, Tokyo Institutue of Technology)
  13. Stochastic Power Law Fluids: the Existence and the Uniqueness of the Weak Solution. (International Workshop on Mathematical Fluid Dynamics, March 13, 2010 at Waseda Univ.) slides.
  14. Branching Random Walks in Random Environment: Survival Probability and Growth Rates, ( The First CREST-SBM International Conference ``Random media'', January 26, 2010 at Seidai International Center). slides.
  15. Stochastic Power Law Fluids: Construction of a Weak Solution. ( 2009年度確率論シンポジウム December 18, 2009 at Ehime Univ.) abstract/ slides.
  16. Stochastic Power Law Fluids: Construction of a Weak Solution. ( Stochastic Problems and Nonlinear PDEs , November 30, 2009, at Kyoto University)
  17. Power Law Fluids with Random Forcing. ( 大規模相互作用系の確率解析, October 9, 2009 at University of Tokyo).
  18. Branching Random Walks in Random Environment: Survival Probability and Growth Rates, ( Topics on Random Media, September 15, 2009 at Kyoto University). slides.
  19. Continuous-Time Linear Systems. ( 統計力学の数学的理論. August 25, 2009 at Osaka Electro-Communication University.) notes available.
  20. Linear Stochastic Evolutions, : Diffusive Behavior and Localization. ( Workshop on Interacting Particle Systems in honour of Professor T. Liggett's 65 th Birthday. June 19, 2009, at Peking University.)
  21. Phase Transitions for Linear Stochastic Evolutions, "Random Syetems and Processes" (February 18, 2009, Kyoto University).
  22. 「ランダム行列で記述される粒子系の相転移」 (2008 年 12月26日 東北大学、 「離散幾何学から提案する新物質創成と 物性発現の解明」キックオフシンポジウム.）
  23. 「ランダム行列で記述される粒子系の相転移」 (2008 年 12月16日 東京工業大学、 「確率論シンポジウム」).
  24. Branching Random Walks in Random Environment: Diffusive Behavior and Localization. (January 14, 2008, at Pontifica Universidad Catolica de Chile, "Workshop on Random Walks, Particle Systems and Random Media").
  25. Branching Random Walks in Random Environment: Diffusive Behavior and Localization. (2007 年 12月12日 熊本大学、 「確率論シンポジウム」).
  26. From Parabolic Anderson Models to Branching Random Walks in Random Environment. (2007 年 12月4日 京都大学 "Stochastic Problems and Nonlinear PDEs").
  27. Branching Random Walks in Random Environment: Diffusive Behavior and Localization. (October 26, 2007, at Nishijin Plaza, Kyusyu University, "Stochastic analysis of large interacting systems").
  28. Central limit theorem for branching random walks in random environment (May 22, 2007, at Oberwolfach "Non-classical interacting random walks").
  29. Branching random walk representation of directed polymers in random environment (2007 年 1月29日 東京工業大学、 「統計物理に関連する数学的話題」).
  30. Directed polymers in random environment (June 16, 2006, at Universite Nantes "EMS Mathematical Week-End").
  31. 「 ランダム媒質中のディレクティドポリマーについて」 (2006 年 3月26日 中央大学、 「日本数学会春期学会」）
  32. Directed polymers in random environment are diffusive at all subcritical tenperature. (September 30, 2005 at RIMS Kyoto "Some Recent Topics on Stochastic Models").
  33. Diffusivity of directed polymers in random environment. (January 31, 2005 at Osaka University Nakanoshima Center "The Fifth East Asia PDE Conference".)
  34. Large time behavior of directed polymers in random environment. (June 27, 2005 at Univ. of California, Santa Barbara, "30 th Stochastic Process and their Applications").
  35. Directed polymers in random environment are diffusive at all subcritical tenperature. (2004 年 12 月 8 日、名古屋大学、「確率論シンポジウム」)
  36. Brownian directed polymers in random environment, (August 31, 2004, at Oberwolfach "Large Scale Stochastic Dynamics").
  37. Localization transition for friendly walkers, (August 20, 2003 at Issac Newton Institute, Cambridge, "Random Walks in Random Environment") Preview
  38. Directed polymers in random environment, (July 24, 2002 at Shonan Village, "Stochastic Analysis on Large Scale Interacting Systems") dvi
  39. Log Sobolev inequalities for unbounded lattice spin systems (Notes for a seminar talk on May 21, 1999 at \'Ecole Polytechnique F\'ed\'erale de Lausanne) dvi
  40. The strong ergodicity for the stochastic dynamics of unbounded lattice spin systems (A note for a seminar talk on September 11, 1998 at Kyushu Univ..) dvi
  41. Log Sobolev inequalities for unbounded lattice spin systems (Notes for a seminar talk on Jun 4, 1998 at Institute Henri Poicare, Paris.) dvi
  42. A note on extremal invariant measures for a Markov process (A note for a seminar talk on May 13, 1998 at Kyoto Univ.) dvi
  43. A central limit theorem for the directed polymer (in Japanese) (A note for a seminar talk on February 6, 1998 at Kyoto Univ.) dvi
  44. Relaxation of kinetic Ising models near the phase transition line (in Japanese) (A note for a talk on Novyemver 17, 1997 at Jyokou-ji meeting.) dvi
  45. On the convergence of finite volume stochastic Ising models, (in Japanese), Notes for a lecture delivered on April 1, 1997 at the annual meeting of Mathematical Scociety of Japan. dvi


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