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1.

図書

図書
E. Bolthausen, E. Perkins, A. van der Vaart ; editor, Pierre Bernard
出版情報: Berlin ; Tokyo : Springer, c2002  viii, 466 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1781
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2.

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:
3.

図書

図書
M. Emery, A. Nemirovski, D. Voiculescu ; editor Pierre Bernard
出版情報: Berlin : Springer, c2000  xi, 349 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1738
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4.

図書

図書
Simon Tavaré, Ofer Zeitouni ; editor, Jean Picard
出版情報: Berlin ; Tokyo : Springer, c2004  314 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1837
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目次情報: 続きを見る
Simon Tavare: Ancestral Inference in Population Genetics Contents / Part I:
Introduction / 1:
The Wright-Fisher model / 2:
The Ewens Sampling Formula / 3:
The Coalescent / 4:
The Infinitely-many-sites Model / 5:
Estimation in the Infinitely-many-sites Model / 6:
Ancestral Inference in the Infinitely-many-sites Model / 7:
The Age of a Unique Event Polymorphism / 8:
Markov Chain Monte Carlo Methods / 9:
Recombination / 10:
ABC: Approximate Bayesian Computation / 11:
Afterwords / 12:
References
Ofer Zeitouni: Random Walks in Random Environment Contents / Part II:
RWRE - d=1
RWRE - d > 1
List of Participants
List of Short Lectures
Simon Tavare: Ancestral Inference in Population Genetics Contents / Part I:
Introduction / 1:
The Wright-Fisher model / 2:
5.

図書

図書
Boris Tsirelson, Wendelin Werner ; editor, Jean Picard
出版情報: Berlin ; Tokyo : Springer, c2004  200 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1840
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6.

図書

図書
J.M. Bismut, L. Gross, K. Krickeberg ; édité par P.L. Hennequin
出版情報: Berlin ; New York : Springer-Verlag, 1982  x, 313 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 929
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7.

図書

図書
R. Azencott, Y. Guivarc'h, R.F. Gundy ; edité par P.L. Hennequin
出版情報: Berlin ; New York : Springer-Verlag, 1980  xiii, 334 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 774
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目次情報: 続きを見る
Introduction
Contexts, reform and resources
Mathematical reasoning through tasks: learners' responses
Learning mathematical reasoning in a collaborative whole class discussion
Classroom practices for teaching and learning mathematical reasoning
Teaching mathematics with the five strands
Teaching the practices of justification and explanation
Learner contributions
Teacher moves
Dilemmas in teaching mathematical reasoning
Learner resistance to mathematical conversations
Introduction
Contexts, reform and resources
Mathematical reasoning through tasks: learners' responses
8.

図書

図書
A. Badrikian, J.F.C. Kingman, J. Kuelbs ; édité par P.-L. Hennequin
出版情報: Berlin ; New York : Springer-Verlag, 1976  ix, 314 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 539
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9.

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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10.

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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