The First Mathematical Society of Japan–Seasonal Institute — Probabilistic Approach to Geometry
July 28–August 8, 2008 | Kyoto University, Japan
Probabilistic Approach to Geometry

Editor(s) Motoko Kotani, Masanori Hino, Takashi Kumagai

Adv. Stud. Pure Math., 57: 514pp. (2010). DOI: 10.2969/aspm/05710000
TABLE OF CONTENTS
View All Abstracts +
Advanced Studies in Pure Mathematics Vol. 57, - (2010).
Advanced Studies in Pure Mathematics Vol. 57, - (2010).
Motoko Kotani , Masanori Hino , Takashi Kumagai
Advanced Studies in Pure Mathematics Vol. 57, - (2010).
Advanced Studies in Pure Mathematics Vol. 57, - (2010).
Advanced Studies in Pure Mathematics Vol. 57, - (2010).
Shigeki Aida
Advanced Studies in Pure Mathematics Vol. 57, 1-28 (2010). https://doi.org/10.2969/aspm/05710001
KEYWORDS: Rough path, stochastic differential equation, 34F05, 60H05, 60H10, 93E03
Marc Arnaudon , Anton Thalmaier
Advanced Studies in Pure Mathematics Vol. 57, 29-48 (2010). https://doi.org/10.2969/aspm/05710029
KEYWORDS: Heat equation, Ricci curvature, Li–Yau inequality, Harnack inequality, gradient bound, Brownian motion, 58J65, 60H30
Atsushi Atsuji
Advanced Studies in Pure Mathematics Vol. 57, 49-59 (2010). https://doi.org/10.2969/aspm/05710049
KEYWORDS: Nevanlinna theory, Brownian motion on Kähler manifolds, Kähler diffusion, value distribution theory, meromorphic functions, 32H30, 58J65
K. David Elworthy
Advanced Studies in Pure Mathematics Vol. 57, 61-78 (2010). https://doi.org/10.2969/aspm/05710061
KEYWORDS: Path space, stochastic analysis, diffeomorphism group, $L^2$ Hodge Theory, Malliavin calculus, Banach manifold, differential forms, curvature, Weitzenböck, symmetric space, Bismut formulae, 58B10, 58J65, 58A14, 60H07, 60H10, 53C17, 58D20, 58B15
Roland Friedrich
Advanced Studies in Pure Mathematics Vol. 57, 79-117 (2010). https://doi.org/10.2969/aspm/05710079
KEYWORDS: Complex variables, stochastic analysis, Conformal Field Theory, 82B99, 32C99, 60J99, 81T40
Ryoki Fukushima , Atsushi Tanida , Kouji Yano
Advanced Studies in Pure Mathematics Vol. 57, 119-128 (2010). https://doi.org/10.2969/aspm/05710119
KEYWORDS: Non-Markov property, random matrix, eigenvalue process, Dyson's model, beta-ensembles, 15A52, 60-06, 60J65, 60J99
Keisuke Hara
Advanced Studies in Pure Mathematics Vol. 57, 129-139 (2010). https://doi.org/10.2969/aspm/05710129
KEYWORDS: Rough path, Fourier transform, 26A45, 42A20
Tae Hattori , Atsushi Kasue
Advanced Studies in Pure Mathematics Vol. 57, 141-153 (2010). https://doi.org/10.2969/aspm/05710141
KEYWORDS: Dirichlet sum of order $p$, Royden compactification, quasi isometry, 53C21, 58D17, 58J50
Yuzuru Inahama
Advanced Studies in Pure Mathematics Vol. 57, 155-170 (2010). https://doi.org/10.2969/aspm/05710155
KEYWORDS: Rough path, stochastic differential equation, 60B12, 58J65, 60J15
Hiroyasu Izeki
Advanced Studies in Pure Mathematics Vol. 57, 171-188 (2010). https://doi.org/10.2969/aspm/05710171
KEYWORDS: Fixed-point property, finitely generated groups, harmonic maps, 58E20, 20F65
Nicolas Juillet
Advanced Studies in Pure Mathematics Vol. 57, 189-198 (2010). https://doi.org/10.2969/aspm/05710189
KEYWORDS: Brunn–Minkowski inequality, curvature-dimension, optimal transport, Heisenberg group, Grušin plane, 28A75, 53C17
Vadim A. Kaimanovich , Florian Sobieczky
Advanced Studies in Pure Mathematics Vol. 57, 199-229 (2010). https://doi.org/10.2969/aspm/05710199
KEYWORDS: Horospheric product, random tree, branching process, graphed equivalence relation, stochastic homogenization, amenability, 37A20, 05C80, 43A07, 60J80
Naotaka Kajino
Advanced Studies in Pure Mathematics Vol. 57, 231-241 (2010). https://doi.org/10.2969/aspm/05710231
KEYWORDS: Generalized Sierpinski carpet, non-diagonality, volume doubling property, self-similar measure, 28A80, 31C25, 60J45
Tsuyoshi Kato
Advanced Studies in Pure Mathematics Vol. 57, 243-262 (2010). https://doi.org/10.2969/aspm/05710243
KEYWORDS: Scale transform, Tropical geometry, discrete dynamical systems, 37E, 39A
Takefumi Kondo
Advanced Studies in Pure Mathematics Vol. 57, 263-272 (2010). https://doi.org/10.2969/aspm/05710263
KEYWORDS: Fixed-point property, random groups, CAT(0) space, 20F67, 20F69, 20P05
Kazumasa Kuwada
Advanced Studies in Pure Mathematics Vol. 57, 273-292 (2010). https://doi.org/10.2969/aspm/05710273
KEYWORDS: Coupling by reflection, synchronous coupling, Ricci curvature, gradient estimate, 60D05, 60H30, 58J65
Kazuhiro Kuwae , Takashi Shioya
Advanced Studies in Pure Mathematics Vol. 57, 293-302 (2010). https://doi.org/10.2969/aspm/05710293
KEYWORDS: Ricci curvature, Bishop–Gromov inequality, 53C20, 53C21, 53C23
Hiroshi Matsuzoe
Advanced Studies in Pure Mathematics Vol. 57, 303-321 (2010). https://doi.org/10.2969/aspm/05710303
KEYWORDS: Statistical manifold, affine differential geometry, information geometry, semi-Weyl manifold, affine distribution, 53A15, 53A30, 53B05, 62B10, 81Q70
Shin-ichi Ohta
Advanced Studies in Pure Mathematics Vol. 57, 323-342 (2010). https://doi.org/10.2969/aspm/05710323
KEYWORDS: Finsler geometry, optimal transport, Ricci curvature, comparison theorem, 53C60, 49Q20, 58J35
Yann Ollivier
Advanced Studies in Pure Mathematics Vol. 57, 343-381 (2010). https://doi.org/10.2969/aspm/05710343
KEYWORDS: Ricci curvature, concentration of measure, Markov chains, Wasserstein distances, metric measure spaces, 51F99, 53B21, 60B99
Vladimir Pestov
Advanced Studies in Pure Mathematics Vol. 57, 383-403 (2010). https://doi.org/10.2969/aspm/05710383
KEYWORDS: Concentration of measure on high-dimensional structures, Polish groups, greatest ambit, Lévy groups, invariant measures, whirly actions, groups of measure-preserving transformations, 37A15, 37B05, 43A05
Laurent Saloff-Coste
Advanced Studies in Pure Mathematics Vol. 57, 405-436 (2010). https://doi.org/10.2969/aspm/05710405
KEYWORDS: Heat kernel, Brownian motion, uniform domains, 58J65, 60J65, 35K05
Ichiro Shigekawa
Advanced Studies in Pure Mathematics Vol. 57, 437-461 (2010). https://doi.org/10.2969/aspm/05710437
KEYWORDS: Non-symmetric diffusion, Riemannian manifold, maximal dissipative operator, generator domain, 58J65, 60J60, 35P15
Asuka Takatsu
Advanced Studies in Pure Mathematics Vol. 57, 463-472 (2010). https://doi.org/10.2969/aspm/05710463
KEYWORDS: Wasserstein space, Gaussian measures, 60D05, 28A33
Sumio Watanabe
Advanced Studies in Pure Mathematics Vol. 57, 473-492 (2010). https://doi.org/10.2969/aspm/05710473
KEYWORDS: Singular regression, real log canonical threshold, singular fluctuation, resolution of singularities, generalization error, 60D05
Kouji Yano
Advanced Studies in Pure Mathematics Vol. 57, 493-503 (2010). https://doi.org/10.2969/aspm/05710493
KEYWORDS: Stable process, conditioning to stay positive, harmonic transform, meander, excursion theory, 60G52, 60F05, 60G17
Takumi Yokota
Advanced Studies in Pure Mathematics Vol. 57, 505-514 (2010). https://doi.org/10.2969/aspm/05710505
KEYWORDS: Ricci flow, reduced volume, asymptotic volume ratio, gradient Ricci soliton, 53C21
Back to Top