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1.

図書

図書
Ivan Cherednik, Peter. J. Forrester [and] Denis Uglov
出版情報: Tokyo : Mathematical Society of Japan, 1998  241 p. ; 25 cm
シリーズ名: MSJ memoirs ; v. 1
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2.

図書

図書
B. Feigin, V. Vassiliev, editors
出版情報: Providence, R.I. : American Mathematical Society, c1998  xiv, 182 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 185 . Advances in the mathematical sciences (formerly advances in Soviet mathematics) ; 38
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3.

図書

図書
editors Sir Michael Atiyah, Daniel Iagolnitzer
出版情報: Singapore : World Scientific : Singapore University Press, c1997  x, 632 p. ; 25 cm
シリーズ名: World Scientific series in 20th century mathematics ; v. 5
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4.

図書

図書
J. Bertoin, F. Martinelli, Y. Peres ; editor, Pierre Bernard
出版情報: Berlin ; Tokyo : Springer, c1999  ix, 289 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1717
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目次情報: 続きを見る
Subordinators Examples and Applications / Jean Bertoin
Foreword / 0:
Elements on subordinators / 1:
Definitions and first properties / 1.1:
The Lévy-Khintchine formula / 1.2:
The renewal measure / 1.3:
The range of a subordinator / 1.4:
Regenerative property / 2:
Regenerative sets / 2.1:
Connection with Markov processes / 2.2:
Asymptotic behaviour of last passage times / 3:
Asymptotic behaviour in distribution / 3.1:
The self-similar case / 3.1.1:
The Dynkin-Lamperti theorem / 3.1.2:
Asymptotic sample path behaviour / 3.2:
Rates of growth of local time / 4:
Law of the iterated logarithm / 4.1:
Modulus of continuity / 4.2:
Geometric properties of regenerative sets / 5:
Fractal dimensions / 5.1:
Box-counting dimension / 5.1.1:
Hausdorff and packing dimensions / 5.1.2:
Intersections with a regenerative set / 5.2:
Equilibrium measure and capacity / 5.2.1:
Dimension criteria / 5.2.2:
Intersection of independant regenerative sets / 5.2.3:
Burgers equation with Brownian initial velocity / 6:
Burgers equation and the Hopf-Cole solution / 6.1:
Brownian initial velocity / 6.2:
Proof of the theorem / 6.3:
Random covering / 7:
Setting / 7.1:
The Laplace exponent of the uncovered set / 7.2:
Some properties of the uncovered set / 7.3:
Levy processes / 8:
Local time at a fixed point / 8.1:
Local time at the supremum / 8.2:
The spectrally negative case / 8.3:
Bochner's subordination for Lévy processes / 8.4:
Occupation times of a linear Brownian motion / 9:
Occupation times and subordinators / 9.1:
Levy measure and Laplace exponent / 9.2:
Lévy measure via excursion theory / 9.2.1:
Laplace exponent via the Sturm-Liouville equation / 9.2.2:
Spectral representation of the Laplace exponent / 9.2.3:
The zero set of a one-dimensional diffusion / 9.3:
Lectures on Glauber Dynamics for Discrete Spin Models / Fabio Martinelli
Introduction
Gibbs Measures of Lattice Spin Models
Notation
Gibbs Measures
Weak and String Mixing Conditions / 2.3:
Mixing properties and bounds on relative densities / 2.4:
The Glauber Dynamics
The Dynamics in Finite Volume
Infinite Volume Dynamics
Graphical Construction / 3.3:
Attractive Dynamics for Ferromagnetic Interactions / 3.4:
Spectral Gap and Logarithmic Sobolev Constant / 3.5:
From Single Spin Dynamics to Block Dynamics / 3.6:
General Results on the Spectral Gap / 3.7:
General Results on the Logarithmic Sobolev Constant / 3.8:
Possible Rates of Convergence to Equilibrium / 3.9:
One Phase Region
The Attractive Case
The General Case Recursive Analysis
Boundary Phase Transitions
The Solid-on-Solid Approximation
Back to the Ising-Model
Recent Progresses / 5.3:
Phase Coexistence
Some Preliminary Key Equilibrium Results
A Geometric Bound on the Spectral Gap
A Lower Bound on the Spectral Gap with + B.C
A Lower Bound on the Spectral Gap with Free B.C / 6.4:
Upper Bound on the Spectral Gap with Free B.C / 6.5:
Mixed B.C / 6.6:
Applications / 6.7:
Glauber Dynamics for the Dilute Ising Model
The Dynamics in the Paramagnetic Phase
The Dynamics in the Griffiths Phase p < pc|
The Dynamics in the Griffiths Phase p = pc
A Coarse Grained Description Above pc / 7.4:
Proof of the Main Results Above pc / 7.5:
Probability on Trees an Introductory Climb / Yuval Peres
Preface
Basic Definitions and a Few Highlights
Galton-Watson Trees
General percolation on a connected graph
The First-Moment Method
Quasi-independent Percolation
The Second Moment Method
Electrical Networks
Infinite Networks
The Method of Random Paths / 10:
Transience of Percolation Clusters / 11:
Subperiodic Trees / 12:
The Random Walks RWλ / 13:
Capacity / 14:
Intersection-Equivalence / 15:
Reconstruction for the Ising Model on a Tree / 16:
Unpredictable Paths in Z and EIT in Z3 / 17:
Tree-Indexed Processes / 18:
Recurrence for Tree-Indexed Markov Chains / 19:
Dynamical Percolation / 20:
Stochastic Domination Between Trees / 21:
Subordinators Examples and Applications / Jean Bertoin
Foreword / 0:
Elements on subordinators / 1:
5.

図書

図書
Andreas Eberle
出版情報: Berlin ; Tokyo : Springer, c1999  viii, 262 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1718
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6.

図書

図書
Kenneth R. Meyer
出版情報: Berlin ; Tokyo : Springer, c1999  ix, 144 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1719
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目次情報: 続きを見る
Introduction / 1:
History / 1.1:
Global vs. Local Notation / 1.2:
Summary of Chapters / 1.3:
Further R eading / 1.4:
Equations of Celestial Mechanics / 2:
N-Body Problem / 2.1:
The Kepler Problem / 2.2:
R estricted Problem / 2.3:
Hill's Lunar Equations / 2.4:
Elliptic Problem / 2.5:
Problems / 2.6:
Hamiltonian Systems / 3:
Symplectic Coordinates / 3.1:
Generating Functions / 3.3:
R otating Coordinates / 3.4:
Jacobi Coordinates / 3.5:
Action-Angle and Polar Coordinates / 3.6:
Solution of the Kepler Problem / 3.7:
Spherical Coordinates / 3.8:
Symplectic Scaling / 3.9:
Central Configurations / 3.10:
Equilibrium Solutions / 4.1:
Equations for a Central Configuration / 4.2:
Relative Equilibrium / 4.3:
Lagrangian Solutions / 4.4:
Euler-Moulton Solutions / 4.5:
Central Configuration Coordinates / 4.6:
Symmetries,Integrals,and Reduction / 4.7:
Group Actions and Symmetries / 5.1:
Systems with Integrals / 5.2:
Noether's Theorem / 5.3:
Integrals / 5.4:
Symplectic R eduction / 5.5:
Reducing the N-Body Problem / 5.6:
Theory of Periodic Solutions / 5.7:
Equilibrium Points / 6.1:
Fixed Points / 6.2:
Periodic Differential Equations / 6.3:
Autonomous Systems / 6.4:
Systems with Symmetries / 6.5:
Hamiltonian Systems with Symmetries / 6.7:
Satellite Orbits / 6.8:
Main Problem for Satellite Problem / 7.1:
Continuation of Solutions / 7.2:
The Restricted Problem / 7.3:
Main Problem for the Three-Bodies / 8.1:
Continuation of Periodic Solutions / 8.2:
Bifurcations of Periodic Solutions / 8.3:
Main Problem for (N + l)-Bodies / 8.4:
R eduction / 8.5:
Lunar Orbits / 8.6:
Main Problem / 9.1:
Continuation / 9.2:
Comet Orbits / 9.3:
Jacobi Coordinates and Scaling / 10.1:
Kepler Problem / 10.2:
R educed Space / 10.3:
The Elliptic Problem / 10.5:
Apollonius Coordinates / 12.1:
Symmetries and R eduction / 12.2:
References / 12.5:
Index
Introduction / 1:
History / 1.1:
Global vs. Local Notation / 1.2:
7.

図書

図書
edited by L. Lovász ... [et al]
出版情報: Budapest : János Bolyai Mathematical Society, 1999  413 p. ; 25 cm
シリーズ名: Bolyai Society mathematical studies ; 7
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8.

図書

図書
[edited by] A.A. Bolibruch, A.S. Merkur'ev, N. Yu. Netsvetaev ; [translation edited by A.B. Sossinsky]
出版情報: Providence, Rhode Island : American Mathematical Society, c1996  xiii, 273 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, vol. 174 . Advances in the mathematical sciences (formerly Advances in Soviet mathematics) ; 30
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9.

図書

図書
edited by O.A. Oleinik ; translated from the Russian by G.A. Yosifan
出版情報: Amsterdam : Gordon and Breach Science Pub., c1996  x, 557 p. ; 24 cm
シリーズ名: Classics of Soviet mathematics ; v. 5 . I.G. Petrowsky selected works ; pt. 1
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10.

図書

図書
edited by O.A. Oleinik ; translated from the Russian by G.A. Yosifan
出版情報: Amsterdam : Gordon and Breach Science Pub., c1996  xii, 501 p. ; 24 cm
シリーズ名: Classics of Soviet mathematics ; v. 5 . I.G. Petrowsky selected works ; pt. 2
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