Hattori, Tetsuya - Mathematical Institute, Tohoku University

• fx(a, b) = lim (f(x, b) -f(a, b)), fy(a, b) (1 )
• Stochastic ranking process with time dependent intensities move-to-front
• 4 hierarchical Ising model ( ) = {i | i } R
• 95CA 95CA X E[ X ] V[ X ] = E[ (X -E[ X ])2
• 2004 11 20 ( ) 11:00-12:30, 14:00-15:00
• Amazon.co.jp (stochastic ranking model)
• Scaling limit of successive approximations for and its consequences on the theories of
• 20050609 13:15-14:45 joint work with F. Comets
• 19980414 0513;14;18;19;21;26;0603; 10(H9 D2);11(S62 D2);18(H2 3);23(H6 9); 24(H6 8);
• 23 1 25 ( ) 5 1 2xy + 2x + y 1, x 0, y 0 xy
• Scalar , fermion , gauge , . 1 Euclidean field theory 4
• 1 B(t) (B(0) = 0) (t > s > 0 B(t) -B(s) B(s), etc.)
• Renormalization group approach to an extension of the law of iterated
• Asymptotic Properties of Branching Symmetric Markov Processes
• lace expansion hara@math.kyushu-u.ac.jp
• (a) Xn, n = 1, 2, 3, , Y L1 (b) [0, 1] Xn,
• Input Output Table http://www.stat.go.jp/data/io/ichiran.htm
• self-avoiding path 1998.41999.3
• 2. 3 self-avoiding path k Wk E[ Wk ] k
• 199806300705;090820;23 30;1021;27;1111;
• shinshu.tex, 1998/7/1417, 90 5
• 5 + 4 sin x V 2001/ 9/12
• 19981108;1202;1212; 2008081619;2228;
• 95CA 95CA : F R {+} F R {+} (
• p. i . -1 7 p.20 .-2 X X Q
• 1998041419981203;1221;19991014; 20050206( platex )09;
• 20010302;04-06;23-27; N = {1, 2, } Z+ = {0, 1, 2, } Z =
• 200605300602 C S1, , Sn S = {S1, , Sn}
• n X1(), , Xn() x = X() E[ X ] = m, V[ X ] = 2
• Stochastic ranking process Amazon.co.jp
• 2005 11 10 ( ) 15:45-17:15 518 Hierarchical Model
• Triviality of hierarchical Ising model in four dimensions Takashi Hara
• The fixed point of a generalization of the renormalization group maps for self-avoiding paths on
• Probability seminar 20050915 thu 15:45-17:15@518 Martin T. Barlow (University of British Columbia)
• Sierpinski gasket abc-gasket Sierpinski gasket Sierpinski carpet
• (x -1)2(x2 + 1) (x -1)(x2 + 2x + 2)
• Random walk and self-avoiding walk (mpshort.tex from III mp.tex)
• Scaling limit of successive approximations for w = -w2
• Stochastic ranking process and web ranking numbers Tetsuya Hattori (Keio University)1
• 1/23 ( ) 14:4516:15 4C hattori@math.nagoya-u.ac.jp
• 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
• Asymptotic behavior of Brownian motions on the hyperbolic spaces
• 2000915;1719;2123;1101(PrbaFubini);08(PrbagenfcnChebishev, PrbaCauchyL1);22(PrbaLpmon);1222;23;
• 2.1 . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
• Hydrodynamic limit of move-to-front rules and search cost probabilities
• Renormalization group analysis of the self-avoiding paths on the d-dimensional Sierpinski gaskets
• 20000420;21;23-30;0503-07;10;15;18-22;25;28;29;0603-08;11-13;15;18-21; 23-0708;10-16; (Tauber) 20000822;24-30; 0912( Feller ); 13( LDP);15; 17 (Intro );
• 3,400,000 0 3,400,000 3,400,000 0 3,400,000
• RIMS K^oky^uroku Bessatsu Bx (200x), 000000
• 20060529mon 16:00-17:00 ( 1970 BlackScholes, Merton
• 2005 (10:3012:00) 201 URL: http://www.math.tohoku.ac.jp/ hattori/hattori.htm
• -Robust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 . . . . . 9
• 1 Wiener 11 1.1 Wiener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
• Estimating Multidimensional Density Functions using the Malliavin-Thalmaier Formula and Application to
• Move-to-front 2007 stochastic ranking process
• 1 (30) R a < b a, b (a, b], (a, ), (-, b), , R,
• 4 hierarchical Ising 2003/01/0810
• Asymptotically one-dimensional diffusions on scale-irregular gaskets.
• 2000101117;22;2527;1107;1214;2230;120105;08;09;1114;2531; 20010101;0608;1125;27;28;020310;13;
• Black-Scholes 2.1 . . . . . . . . . . . . . . . . . . . . 5
• 1 (30) R 0 0 1 B 0 B 0(B) = 1 0 B 0(B) = 0 1
• a1, , ak a1, , ak 1 1 Ax = 0 V = {x Rn | Ax = 0}
• Citation Statistics SPARC JAPAN
• 2000060610;13;1719;0713;15;19;20; 29.4 2] (L1
• (s, t) = ((2 + t cos ) sin s, (2 + t cos
• 1999122528;20050708 [4, 5] formulate
• FritzJohn Gordan A n m (1)(2)
• Renormalization group approach to a generalization of the law of iterated logarithms for one-dimensional
• 20051027( )16:00-17:30 801 Markov chain technical
• MathMLMathematica TeXWordMathML
• Renormalization group approach to an extension of the law of iterated logarithms for one-dimensional
• Stochastic ranking process 2ch.net Amazon.co.jp
• 20010412;20;23;25;280507;0919;0917-19;22;23;1017;1127;1204; 20020108;15; 20061107;
• 2005 (10:3012:00) C406 10, 12, 13, 14
• 2008 (6/10-13) 2 a(x), b(x) R (0, )
• t (x1(t), x2(t), x3(t)) i = 1, 2, 3
• 2007.11.1619,12.04 27 8 (1.18) M
• [34, 29, 30, 31, 32, 42, 37, 43, 6, 7, 17, 26] [20] (self-avoiding path) [34, 27, 25, 39, 28, 41, 38]
• self-avoiding path 1 W(x, y) = a x3
• Renormalization group approach to a generalization of the law of iterated logarithms for one-dimensional (non-Markovian)
• d self-avoiding path (canonical surface) (fixed point)
• Zd sample( ) Zd EN [] = ZN (T )-1
• 4. Z self-repelling walk F. B. Knight (1962)
• d self-avoiding walk SAW mean square displacement exponent
• pre-history of processes on fractals 1985/4/n a seminar talk by T.H.
• self-avoiding path dSG (d pre-gasket) d = 2, 3, 4,
• On a limit theorem for non-stationary branching processes.
• Stochastic ranking process ( ) 1 , , X
• Amazon.co.jp Amazon.co.jp
• STOCHASTIC RANKING PROCESS WITH TIME DEPENDENT INTENSITIES
• Mathematical analysis of long tail economy using stochastic ranking Kumiko Hattori
• Equation of motion for incompressible mixed fluid driven by evaporation and its application to online rankings
• Existence of an infinite particle limit of stochastic ranking process Kumiko Hattori
• Celebrating Professor K. R. Ito and Professor I. Ojima on their 60th Tetsuya Hattori (Keio Univ.)
• ( ) 5. (2) 1 199804141209;
• 199804140609;10;11;18;23;24;1018( ); 20050207( platex );08( )10;
• A note on a scaling limit of successive approximation for a differential equation with moving singularity.
• A limit theorem for BohrJessen's probability measures of the Riemann zeta-function.
• 1 (40) N(0, 1) x x P[ [x, ) ] 4
• 2004060713;15;2030;070102;0406;0710;13;0911;28;20050815( ); http:/www.math.tohoku.ac.jp/~hattori/gakjutu.htm
• http:/www.math.tohoku.ac.jp/~hattori/gakjutu.htm 19960107;27;30 etc.;0410;1316;21;27-30;0501;03-16;18;19-20(rnd);21-23;
• 1995.41995.6 Z 0 < Z < 10
• (0), (1, 2), (-1, 0, 1, 0, 1, 2) (w(0), w(1), , w(k)) Z path
• 1/24 ( ) 09:3011:30 309 ([37][72])
• 12/13 ( ) 09:3011:00 309 (i) [19][36]
• 95CA 95CA A Ac A, B A Bc A \ B
• 94CA 94CA 1. 6 = {1, 2, 3, 4, 5, 6}
• 2001091622;1017;23;20020108;15;20; N = {1, 2, } Z+ = {0, 1, 2, } Z =
• (1) --(10) (0) 5 (1)(4)(7)(10) n2 + 1 -n) = lim
• U = U(x), x: marginal utility "law" of diminishing marginal utility
• U = U(x), x: marginal utility "law" of diminishing marginal utility
• 1999011619990525kiso.tex kiso1 kiso2 19990615;0705;0709;12;13;19;20;24;25;080306;10;1221;
• 12/12 ( ) 14:4516:15 4C (i) (4.1, 4.2, 4.3)
• 2005/05/30-06/03 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
• [1] Lamberton, D. & B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall, 1996.
• Danwa-kai, Wednesday June 29, Kyoto Old and recent topics on the subject of resolution of singularities
• Amazon.co.jp Amazon.co.jp
• SPARC Japan>> 20(2008)93()
• RIMS 8&5f =82q!V5*MW$NEE;R2=$H<~JU$NOCBj!W 6&:E SPARC JAPAN O"B3%;%_%J!<
• RIMS2008 K.Hayashi SPARC JAPAN
• 2 2008 10 25 ,21 3 B S B T
• 2.1 . . . . . . . . . . . . . . . . . . . . . . 6 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
• Differentiability of Spectral Functions for Symmetric Markov Processes
• [1] [AK] APPLEBAUM, DAVID AND KUNITA, HIROSHI (1993). Levy flows on manifolds and Levy processes on Lie
• (F. Comets, T. Shiga, N. Yoshida [2]) (F. Comets, N. Yoshida [1]) . [1]
• Essential self-adjointness of Dirichlet operators on a path space
• Stochastic PDEs driven by space-time white noise
• 20050915( ) 15:45-17:15@518 Martin T. Barlow British Columbia
• 20050707 15:45-17:15 Brox (1986), Schumacher (1985)
• 2004 11 20 ( ) 11:00-12:30, 14:00-15:00
• kaiseki1.lec(tex) 1995122819960131;020414;1626;0329;
• Self-avoiding Paths on the Three Dimensional Sierpinski Gasket
• 19990116;27;0203;07;1520;23;24;28;0311;14;15;30;31;041012;25; 050106;19;20;2325;0714;20;0813; 20000418;25;0509;16;19;20;23;30;0613;20;27;0704;18;
• Running Head: Displacement exponent of self-repelling walks 1 Displacement exponents of self-repelling walks and self-attracting
• IMPROVEMENT OF EFFICIENCY IN GENERATING RANDOM U(1) VARIABLES
• Mathematical Derivation of Chiral Anomaly in Lattice Gauge Theory with Wilson's Action
• {0, 1, 2, , n} (ai)0in (bi)0in ai, bi > 0, ai + bi 1 a0 = 0, bn = 0
• 1995.41995.6 1995.41995.6
• 3. (1) Fubini 1 199804141209;1212;1215;
• Constructive field theory and renormalization group Hiroshi WATANABE 1
• A hydrodynamic limit of move-to-front rules and its application to web rankings
• 2005020810;12; 200808270916;
• dx , x > 0, n = 0, 1, 2, , (1) w0(x) = x-1
• self-avoiding path dSG self-avoiding path
• Transition density of diffusion on Sierpinski gasket and extension of Flory's formula Tetsuya Hattori
• 3. (1) Fubini 1 1998110819981204;1214;1215;
• (X, B, ) f {f : X C | f p < } Banach
• 20041213mon14:00-15:30 202 with Barlow--Bass, and with Barlow--Coulhein
• 2011.07.1922 1 , , X
• Date: 2011. 11. 30. Parabolic Reduction, Stability and Volumes of Funda-
• 11 0 < p < 1 p n = {(0, 0, . . . , 0), (1, 0, . . . , 0), . . . , (1, 1, . . . , 1)}
• p.15 1.1(2) A A a(a = 1) q , q = ap
• 13 100 100 100 1 1 100