Preprints

M. Biskup and T. Kumagai,
Quenched invariance principle for a class of random conductance models with long-range jumps.
PDF File

M.T. Barlow, D.A. Croydon and T. Kumagai,
Subsequential scaling limits of simple random walk on the two-dimensional uniform spanning tree.
PDF File

T. Kumagai, Anomalous random walks and diffusions: From fractals to random media.
Proceedings of 2014 ICM, Seoul. PDF File

Z.-Q. Chen, D.A. Croydon and T. Kumagai,
Quenched invariance principles for random walks and elliptic diffusions in random media with boundary.
Ann. Probab., to appear. (Revised Version) PDF File

T. Kumagai and Zeitouni,
Fluctuations of recentered maxima of discrete Gaussian Free Fields on a class of recurrent graphs.
Electron. Commun. Probab., 18 (2013), no. 75, 1--12. Go to ECP

K. Bogdan, T. Kumagai and M. Kwaśnicki,
Boundary Harnack inequality for Markov processes with jumps.
Trans. Amer. Math. Soc., to appear. (Revised Version) PDF File

The author would appreciate any comments on manuscripts.


Book

T. Kumagai, Random Walks on Disordered Media and their Scaling Limits.
Lecture Notes in Mathematics, Vol. 2101, École d'Été de Probabilités de Saint-Flour XL--2010.
Springer, New York, (2014).

Refereed Papers

59) D.A. Croydon, A. Fribergh and T. Kumagai,
Biased random walk on critical Galton-Watson trees conditioned to survive.
Probab. Theory Relat. Fields, 157 (2013), 453--507. (Rev\ ised Version) PDF File (277kb)

58) J.-D. Deuschel and T. Kumagai,
Markov chain approximations to non-symmetric diffusions with bounded coefficients.
Comm. Pure Appl. Math. 66 (2013), no. 6, 821--866. (Revised Version) PDF File (292kb)

57) Z.-Q. Chen, P. Kim and T. Kumagai,
Discrete Approximation of Symmetric Jump Processes on Metric Measure Spaces.
Probab. Theory Relat. Fields 155 (2013), 703--749. (Revised Version) PDF File (430kb)

56) M.T. Barlow, A. Grigor'yan and T. Kumagai,
On the equivalence of parabolic Harnack inequalities and heat kernel estimates.
J. Math. Soc. Japan, 64 (2012), no. 4, 1091--1146. (Revised Version) PDF File (714kb)

55) D.A. Croydon, B.M. Hambly and T. Kumagai,
Convergence of mixing times for sequences of random walks on finite graphs.
Electron. J. Probab., 17 (2012), no. 3, 1--32. Go to EJP

54) Z.-Q. Chen, P. Kim and T. Kumagai,
Global Heat Kernel Estimates for Symmetric Jump Processes.
Trans. Amer. Math. Soc., 363 (2011), no. 9, 5021--5055. (Revised Version) PDF File (569kb) PS File (1897kb)

53) R.F. Bass, T. Kumagai and T. Uemura,
Convergence of symmetric Markov chains on Zd.
Probab. Theory Relat. Fields, 148 (2010), 107--140. (Revised Version) PDF File (252kb) PS File (552kb) Correction PDF File (68Kb)

52) Z.-Q. Chen and T. Kumagai,
A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps.
Rev. Mat. Iberoamericana, 26 (2010), 551--589. PDF File (289kb) PS File (1268kb)

51) M.T. Barlow, R.F. Bass, T. Kumagai and A. Teplyaev,
Uniqueness of Brownian motion on Sierpinski carpets.
J. European Math. Soc., 12 (2010), 655--701. PDF File (368kb) PS File (761kb)

* Supplementary notes for "Uniqueness of Brownian motion on Sierpinski carpets"
(joint with M.T. Barlow, R.F. Bass and A. Teplyaev), PDF File (223kb) PS File (518kb)

50) B.M. Hambly and T. Kumagai,
Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice.
Comm. Math. Phys., 295 (2010), 29--69. PDF File (392kb) PS File (1966kb)

49) R.F. Bass, M. Kassmann and T. Kumagai,
Symmetric jump processes: localization, heat kernels, and convergence.
Ann. Inst. H. Poincaré - Probabilités et Statistiques, 46 (2010), 59--71. PDF File (160kb) PS File (365kb)

48) Z.-Q. Chen, P. Kim and T. Kumagai,
On Heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces.
Acta Math. Sin. (Engl. Ser.) 25 (2009), 1067--1086. PDF File (206kb) PS File (485kb)

47) M.T. Barlow, R.F. Bass and T. Kumagai,
Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps.
Math. Z. 261 (2009), no. 2, 297--320. PDF File (208kb), Post Script File. (458kb)

46) M.T. Barlow, A. Grigor'yan and T. Kumagai,
Heat kernel upper bounds for jump processes and the first exit time.
J. Reine Angew. Math. 626 (2009), 135--157. PDF File (318kb), Post Script File. (779kb) Corrections PDF File (104Kb)

45) T. Kumagai and J. Misumi,
Heat kernel estimates for strongly recurrent random walk on random media.
J. Theoret. Probab. 21 (2008), no. 4, 910--935. (Revised Version) PDF File (221kb), Post Script File. (498kb)

44) Z.-Q. Chen, P. Kim and T. Kumagai,
Weighted Poincaré inequality and heat kernel estimates for finite range jump processes.
Math. Ann., 342, (2008), no. 4, 833--883. PDF File (278kb), PS File (1366kb)

43) A. Grigor'yan anf T. Kumagai,
On the dichotomy in the heat kernel two sided estimates.
In: Analysis on Graphs and its Applications (P. Exner et al. (eds.)), Proc. of Symposia in Pure Math. 77,
pp. 199--210, Amer. Math. Soc. 2008. PDF File (169kb), PS File (454kb)

42) D. Croydon and T. Kumagai,
Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive.
Electron. J. Probab., 13 (2008), 1419--1441. Go to EJP

41) T. Kumagai,
Recent developments of analysis on fractals.
Translations, Series 2, Volume 223, pp. 81--95, Amer. Math. Soc. 2008.
PDF File (381kb), Post Script File. (2270kb)

40) M.T. Barlow, A.A. Járai, T. Kumagai and G. Slade,
Random walk on the incipient infinite cluster for oriented percolation in high dimensions.
Comm. Math. Phys., 278 (2008), no 2, 385--431.
PDF File (434kb), Post Script File. (897kb)

39) I. Fujii and T. Kumagai,
Heat kernel estimates on the incipient infinite cluster for critical branching processes.
Proceedings of German-Japanese symposium in Kyoto 2006,
RIMS Kôkyûroku Bessatsu B6 (2008), 85--95 PDF File (138kb), Post Script File. (359kb)

38) R.F. Bass and T. Kumagai,
Symmetric Markov chains on Zd with unbounded range.
Trans. Amer. Math. Soc., 360 (2008), no. 4, 2041--2075. PDF File (525kb), Post Script File. (558kb)

37) Z.-Q. Chen and T. Kumagai,
Heat kernel estimates for jump processes of mixed types on metric measure spaces.
Probab. Theory Relat. Fields, 140 (2008), no. 1-2, 277--317. PDF File (440kb), Post Script File. (517kb)

36) J. Hu and T. Kumagai,
Nash-type inequalities and heat kernels for non-local Dirichlet forms.
Kyushu J. Math., 60 (2006), no.2, 245--265. Post Script File. (328kb)

35) M.T. Barlow and T. Kumagai,
Random walk on the incipient infinite cluster on trees.
Illinois J. Math., 50 (2006), no.1, 33--65. (Doob volume) PDF File (308kb),Post Script File. (414kb)

34) M. Hino and T. Kumagai,
A trace theorem for Dirichlet forms on fractals.
J. Func. Anal., 238 (2006), no.2, 578--611. PDF File (613kb),Post Script File. (2021kb)

33) M.T. Barlow, R.F. Bass and T. Kumagai,
Stability of parabolic Harnack inequalities on metric measure spaces.
J. Math. Soc. Japan, 58 (2006), no. 2, 485--519. PDF File (401kb), Post Script File. (1431kb)

*Note on the equivalence of parabolic Harnack inequalities and heat kernel estimates
(joint with M.T. Barlow and R.F. Bass), Post Script File. (235kb)

32) M.T. Barlow, T. Coulhon and T. Kumagai,
Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs.
Comm. Pure Appl. Math., 58 (2005), no. 12, 1642--1677. PDF File (249kb), Post Script File. (357kb)

31) K.T. Sturm and T. Kumagai,
Construction of diffusion processes on fractals, d-sets, and general metric measure spaces.
J. Math. Kyoto Univ. 45 (2005), no. 2, 307--327. Post Script File. (317kb)

30) B.M. Hambly and T. Kumagai,
Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometries.
In: Fractal geometry and applications: A Jubilee of B. Mandelbrot (M.L. Lapidus and M. van Frankenhuijsen (eds.)),
Proc. of Symposia in Pure Math. 72, Part 2, pp. 233--260, Amer. Math. Soc. 2004. PDF File (343kb), Post Script File. (540kb)

29) T. Kumagai,
Recent developments of analysis on fractals (in Japanese).
"Sugaku", Iwanami-shoten, 56 (2004), no.4, 337--350.

28) T. Kumagai,
Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms.
Publ. RIMS, Kyoto Univ., 40 (2004), 793--818. Post Script File. (309kb) Corrections PDF File. (757Kb)

27) T. Kumagai,
Function spaces and stochastic processes on fractals.
In: Fractal geometry and stochastics III (C. Bandt et al. (eds.)), Progr. Probab. 57, pp. 221--234,
Birkhauser, 2004. Post Script File. (267kb)

26) B.M. Hambly and T. Kumagai,
Heat kernel estimates and law of the iterated logarithm for symmetric random walks on fractal graphs.
In: Discrete Geometric Analysis, (M. Kotani et al. (eds.)), Contemporary Mathematics 347, pp. 153--172,
Amer. Math. Soc. 2004. PDF File (301kb), Post Script File. (351kb)

25) T. Kumagai,
Homogenization on finitely ramified fractals.
Advanced Studies in Pure Math., 41, Stochastic Analysis and Related Topics in Kyoto (H. Kunita et al. (eds.)),
pp. 189--207, MSJ, 2004. PDF File (248kb), Post Script File. (270kb)

24) B.M. Hambly and T. Kumagai,
Diffusion processes on fractal fields: heat kernel estimates and large deviations.
Probab. Theory Relat. Fields, 127 (2003), no.3, 305--352.
PDF File (609kb), Post Script File. (1936kb)

23) Z.-Q. Chen and T. Kumagai,
Heat kernel estimates for stable-like processes on d-sets.
Stoch. Proc. Their Appl., 108 (2003), no. 1, 27--62. PDF File (363kb), Post Script File. (459kb)

22) T. Kumagai,
Some remarks for stable-like jump processes on fractals.
In: Trends in Math., Fractals in Graz 2001 (P. Grabner and W. Woess (eds.)),
pp. 185-196, Birkhauser, 2002. Post Script File (210kb), Dvi file.(54kb)

21) B.M. Hambly and T. Kumagai,
Asymptotics for the spectral and walk dimension as fractals approach Euclidean space.
Fractals, 10 (2002), no. 4, 403--412. PDF File. (230kb)

20) R.F. Bass and T. Kumagai,
Laws of the iterated logarithm for the range of random walks in two and three dimensions.
Ann. Probab., 30 (2002), no. 3, 1369--1396. Dvi file. (107kb)

19) B.M. Hambly, J. Kigami and T. Kumagai,
Multifractal formalisms for the local spectral and walk dimensions.
Math. Proc. Cambridge Philos. Soc., 132 (2002), no. 3, 555--571. Dvi file. (Revised Draft, 80kb)

18) M.T. Barlow and T. Kumagai,
Transition density asymptotics for some diffusion processes with multi-fractal structures.
Electronic Journal of Probability, (paper 9) 6 (2001), 1--23. Go to EJP

17) B.M. Hambly and T. Kumagai,
Fluctuation of the transition density for Brownian motion on random recursive Sierpinski gaskets.
Stoch. Proc. Their Appl., 92 (2001), no. 1, 61--85. Post Script File. (439kb)

16) R.F. Bass and T. Kumagai,
Laws of the iterated logarithm for some symmetric diffusion processes.
Osaka J. Math., 37 (2000), no. 3, 625--650. Dvi file. (102kb)

15) B.M. Hambly, T. Kumagai, S. Kusuoka and X.Y. Zhou,
Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets.
J. Math. Soc. Japan, 52 (2000), no. 2, 373--408. Post Script File. (1643Kb)

14) T. Kumagai,
Stochastic processes on fractals and related topics.
Sugaku Expositions, Amer. Math. Soc., 13 (2000), no. 1, 55--71.

13) G. Ben Arous and T. Kumagai,
Large deviations for Brownian motion on the Sierpinski gasket.
Stoch. Proc. Their Appl., 85 (2000), 225--235. Dvi file. (49kb)

12) T. Kumagai,
Brownian motion penetrating fractals -An application of the trace theorem of Besov spaces-.
J. Func. Anal., 170 (2000), no. 1, 69--92. Dvi File. (103Kb) Corrections Dvi File. (2Kb)

11) B.M. Hambly and T. Kumagai,
Transition density estimates for diffusion processes on p.c.f. self-similar fractals.
Proc. London Math. Soc., 78 (1999), no. 3, 431--458.

10) B.M. Hambly and T. Kumagai,
Heat kernel estimates and homogenization for asymptotically lower dimensional processes on some nested fractals.
Potential Anal., 8 (1998), 359--397.

9) T. Kumagai,
Stochastic processes on fractals and related topics (in Japanese).
"Sugaku", Iwanami-shoten, 49 (1997), no. 2, 158--172.

8) T. Kumagai,
Short time asymptotic behavior and large deviations for Brownian motion on some affine nested fractals.
Publ. RIMS. Kyoto Univ., 33 (1997), 223--240.

7) T. Kumagai,
Percolation on pre-Sierpinski carpets.
In: New trends in stochastic analysis -Proceedings of a Taniguchi International Workshop (K.D.Elworthy et al (eds.)),
World Scientific, 1997, pp. 288-304.

6) T. Kumagai and S. Kusuoka,
Homogenization on nested fractals.
Probab. Theory Relat. Fields, 104 (1996), 375--398.

5) T. Kumagai,
Rotation invariance and characterization of a class of self-similar diffusion processes on the Sierpinski gasket.
In: Algorithms, fractals, and dynamics (Y.Takahashi (ed.) ), Plenum, 1995, pp. 131--142.

4) P.J. Fitzsimmons, B.M. Hambly and T. Kumagai,
Transition density estimates for Brownian motion on affine nested fractals.
Comm. Math. Phys., 165 (1994), no. 3, 595--620.

3) T. Kumagai,
Estimates of transition densities for Brownian motion on nested fractals. (Ph.D. thesis)
Probab. Theory Relat. Fields, 96 (1993), 205--224.

2) T. Kumagai,
Regularity, closedness and spectral dimensions of the Dirichlet forms on P.C.F. self-similar sets.
J. Math. Kyoto Univ., 33 (1993), 765--786.

1) T. Kumagai,
Construction and some properties of a class of non-symmetric diffusion processes on the Sierpinski gasket.
In: Asymptotic problems in probability theory: stochastic models and diffusions on fractals (Elworthy, K.D. and Ikeda, N.
(eds.)), Pitman, 1993, pp. 219--247.



Other Papers in English

4) T. Kumagai,
Brownian motions on fractals.
Bulletin de liaison, No. 7 (2004), 1--17. Post Script File. (1021kb) Go to Bulletin

3) T. Kumagai,
Function spaces and stochastic processes on fractals.
S\=urikaisekikenky\=usho K\=oky\=uroku, No. 1293 (2002), 42--54.

2) T. Kumagai,
Construction of diffusion processes penetrating fractals
-An application of the theory of Besov spaces-.
S\=urikaisekikenky\=usho K\=oky\=uroku, No. 1235 (2001), 91--114.

1) T. Kumagai,
Estimates of transition densities for Brownian motion on nested fractals.
S\=urikaisekikenky\=usho K\=oky\=uroku, No. 783 (1992), 27--45.

Articles written in Japanese

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