Self-Similar Markov Trees and Scaling Limits

Inbunden, Engelska, 2027

Del 12 i serien Institute of Mathematical Statistics Monographs

800 kr

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Beskrivning

Self-similar Markov trees form a remarkable family of random compact real trees equipped with a decoration function that is positive on the skeleton, encompassing the Brownian continuum random tree, stable Lévy trees, fragmentation trees, and growth-fragmentation trees. In this book, the authors develop a consistent and unified theory of self-similar Markov trees by bringing together and vastly generalizing results that had been scattered across the random tree literature over several decades. They begin with in-depth coverage of the construction of self-similar Markov trees, then address the study of self-similar Markov trees in the continuous. In Part II, the authors build on this material and introduce readers to current research. They establish general invariance principles for Galton-Watson trees with integer types and illustrate them through numerous combinatorial classes of random trees that have appeared in the literature.

Produktinformation

Utgivningsdatum:2027-02-28
Format:Inbunden
Språk:Engelska
Serie:Institute of Mathematical Statistics Monographs
Antal sidor:340
Förlag:Cambridge University Press
ISBN:9781009772082

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Jean Bertoin is Professor at the University of Zurich. He has previously authored two books published by Cambridge – 'Lévy Processes' (1996) and 'Random Fragmentation and Coagulation Processes' (2006). He is a member of the European Academy of Sciences and a corresponding member of the Mexican Academy of Sciences. Nicolas Curien is Professor at Université Paris-Saclay since 2014. His research focuses on probability theory and the geometry of random structures such as planar maps and random surfaces. He is a recipient of several international prizes, and a member of several gastronomic societies. Armand Riera is Associate Professor at Sorbonne University since 2022. His research focuses on stochastic processes and the geometry of large random structures such as trees, planar maps, and random surfaces.

Innehållsförteckning

Notation and Terminology; 1. Introduction; Part I. Self-Similar Markov Trees: 2. Decorated real trees; 3. Branching processes with real types; 4. Examples; 5. Markov properties; 6. Spinal decompositions and bifurcators; Part II. Discrete Markov Branching Trees: 7. Galton–Watson processes with integer types and their scaling limits; 8. Analytical criteria for the invariance principle; 9. Applications; Appendix. Technical results; References; Index.