| List of contributors | p. xiii |
| Preface | p. xv |
| Bibliography of | p. 1 |
| A fragment of autobiography, 1957-1967 | p. 17 |
| More uses of exchangeability: representations of complex random structures | p. 35 |
| Introduction | p. 35 |
| Exchangeability | p. 36 |
| Using exchangeability to describe complex structures | p. 43 |
| Construction of, and convergence to, infinite random combinatorial objects | p. 49 |
| Limits of finite deterministic structures | p. 56 |
| Miscellaneous comments | p. 59 |
| Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding | p. 64 |
| Introduction | p. 64 |
| Perfect simulation | p. 66 |
| Area-interaction processes | p. 71 |
| Nonparametric regression by wavelet thresholding | p. 77 |
| Perfect simulation for wavelet curve estimation | p. 82 |
| Conclusion | p. 88 |
| Assessing molecular variability in cancer genomes | p. 91 |
| Introduction | p. 91 |
| Colorectal cancer data | p. 93 |
| The Ewens sampling formula | p. 95 |
| Analysis of the cancer data | p. 98 |
| Poission approximation | p. 100 |
| Conclusion | p. 110 |
| Branching out | p. 113 |
| Introduction | p. 113 |
| The basic model | p. 115 |
| Spreading out: old results | p. 116 |
| Spreading out: first refinements | p. 119 |
| Spreading out: recent refinements | p. 120 |
| Deterministic theory | p. 122 |
| The multitype case | p. 124 |
| Anomalous spreading | p. 125 |
| Discussion of anomalous spreading | p. 130 |
| Kingman, category and combinatorics | p. 135 |
| Introduction | p. 135 |
| Preliminaries | p. 138 |
| A bitopological Kingman theorem | p. 143 |
| Applications-rational skeletons | p. 151 |
| KBD in van der Waerden style | p. 157 |
| Applications: additive combinatorics | p. 162 |
| Long-range dependence in a Cox process directed by an alternating renewal process | p. 169 |
| Preamble | p. 170 |
| Introduction | p. 170 |
| Stationary renewal and alternating renewal processes | p. 172 |
| Second moments | p. 178 |
| An alternating renewal process not satisfying Condition A | p. 180 |
| Postlude | p. 181 |
| Kernel methods and minimum contrast estimators for empirical deconvolution | p. 185 |
| Introduction | p. 186 |
| Methodology and theory | p. 191 |
| Relationship to minimum contrast methods | p. 195 |
| The coalescent and its descendants | p. 204 |
| Introduction | p. 205 |
| The coalescent and the Fleming-Viot process | p. 206 |
| Inference under the coalescent | p. 213 |
| The Li and Stephens model | p. 215 |
| Application: modelling population structure | p. 221 |
| Kingman and mathematical population genetics | p. 238 |
| Introduction | p. 238 |
| Background | p. 239 |
| Putting it together | p. 244 |
| Robustness | p. 247 |
| A convergence result | p. 248 |
| Partition structures | p. 249 |
| 'Age' properties and the GEM distribution | p. 251 |
| The coalescent | p. 256 |
| Other matters | p. 260 |
| Characterizations of exchangeable partitions and random discrete distributions by deletion properties | p. 264 |
| Introduction | p. 265 |
| Partition structures | p. 266 |
| Partially exchangeable partitions | p. 274 |
| Exchangeable partitions | p. 278 |
| The deletion property without the regularity condition | p. 285 |
| Regeneration and -deletion | p. 286 |
| Applying coupon-collecting theory to computer-aided assessments | p. 299 |
| Introduction | p. 299 |
| Coupon collecting | p. 300 |
| How many tests? | p. 302 |
| Asymptotics | p. 303 |
| Proofs for §4 | p. 305 |
| Numerical results | p. 314 |
| Discussion | p. 315 |
| Colouring and breaking sticks: random distributions and heterogeneous clustering | p. 319 |
| Introduction | p. 319 |
| Mixture models and the Dirichlet process | p. 320 |
| Applications and generalisations | p. 325 |
| Pólya urn schemes and MCMC samplers | p. 329 |
| A coloured Dirichlet process | p. 333 |
| The associated random walk and martingales in random walks with stationary increments | p. 345 |
| Introduction and definition | p. 345 |
| Three examples | p. 349 |
| Some remarks on duality and asymptotic independence | p. 355 |
| Diffusion processes and coalescent trees | p. 358 |
| Introduction | p. 359 |
| A coalescent dual process | p. 361 |
| Processes with beta stationary distributions and Jacobi polynomial eigenfunctions | p. 368 |
| Subordinated Jacobi diffusion processes | p. 371 |
| Subordinated coalescent process | p. 375 |
| Three problems for the clairvoyant demon | p. 380 |
| Introduction | p. 380 |
| Site percolation | p. 381 |
| Clairvoyant scheduling | p. 383 |
| Clairvoyant compatibility | p. 384 |
| Clairvoyant embedding | p. 385 |
| Dependent percolation | p. 390 |
| Percolation of words | p. 393 |
| Homogenization for advection-diffusion in a perforated domain | p. 397 |
| Introduction | p. 398 |
| Review of homogenization for diffusion with periodic drift | p. 400 |
| Existence of a volume growth rate for a diffusion sausage with periodic drift | p. 402 |
| Estimates for the diffusion sausage | p. 403 |
| Asymptotics of the growth rate for small and large cross-sections | p. 405 |
| Homogenization of the advection-diffusion equation in a perforated domain | p. 408 |
| The case of diffusivity 2I | p. 410 |
| Monte Carlo computation of the asymptotic growth rate | p. 411 |
| Heavy traffic on a controlled motorway | p. 416 |
| Introduction | p. 416 |
| A single queue | p. 418 |
| A model of Internet congestion | p. 422 |
| A Brownian network model | p. 426 |
| A model of a controlled motorway | p. 430 |
| Route choices | p. 438 |
| Concluding remarks | p. 442 |
| Coupling time distribution asymptotics for some couplings of the Lévy stochastic area | p. 446 |
| Different kinds of couplings | p. 448 |
| Reflection coupling | p. 450 |
| Coupling more than one feature of the process | p. 451 |
| Conclusion | p. 461 |
| Queueing with neighbours | p. 464 |
| Introduction | p. 464 |
| Results | p. 467 |
| Asymmetric interaction | p. 470 |
| Symmetric interaction | p. 475 |
| Appendix | p. 480 |
| Optimal information feed | p. 483 |
| Interrogation, transmission and coding | p. 483 |
| A tractable infinite-horizon case | p. 486 |
| A dynamical-system picture of a simple branching-process phase transition | p. 491 |
| Introduction | p. 491 |
| Wiener-Hopferization | p. 493 |
| How does ODE theory see the phase transition? | p. 496 |
| Proof of Theorem 1.1 and more | p. 499 |
| Index | p. 509 |
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