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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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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:
2.

図書

図書
R. M. Dudley, H. Kunita, F. Ledrappier ; édité par P. L. Hennequin
出版情報: Berlin ; New York : Springer-Verlag, 1984.  x, 396 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1097
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3.

図書

図書
E. Giné, G.R. Grimmett, L. Saloff-Coste ; editor, P. Bernard
出版情報: Berlin : Springer, c1997  x, 424 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1665
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4.

図書

図書
X. Fernique ... [et al.] ; edité par P.L. Hennequin
出版情報: Berlin ; New York : Springer-Verlag, c1983  xi, 465 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 976
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5.

図書

図書
Terry J. Lyons, Michael Caruana, Thierry Lévy
出版情報: Berlin : Springer, c2007  xviii, 109 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1908 . École d'été de probabilités de Saint-Flour / editor, Jean Picard ; 34-2004
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