Genealogies of Interacting Particle Systems

Interacting particle systems are Markov processes involving infinitely many interacting components. Since their introduction in the 1970s, researchers have found many applications in statistical physics and population biology. Genealogies, which follow the origin of the state of a site backwards in time, play an important role in their studies, especially for the biologically motivated systems.

The program Genealogies of Interacting Particle Systems held at the Institute for Mathematical Sciences, National University of Singapore, from 17 July to 18 Aug 2017, brought together experts and young researchers interested in this modern topic. Central to the program were learning sessions where lecturers presented work outside of their own research, as well as a normal workshop. This is reflected in the present volume which contains two types of articles:

Written by respected researchers, including experts in the field such as Steve Evans, member of the US National Academy of Sciences, as well as Anton Wakolbinger, Andreas Greven, and many others, this volume will no doubt be a valuable contribution to the probability community.
Contents: Lecture Notes from Learning Sessions:Coexistence and Duality in Competing Species Models (Yu-Ting Chen and Matthias Hammer)Stochastic Evolution of Genealogies of Spatial Populations: State Description, Characterization of Dynamics and Properties (Andrej Depperschmidt and Andreas Greven)The Algebraic Approach to Duality: An Introduction (Anja Sturm, Jan M Swart and Florian Völlering)The Genealogy of Extremal Particles of Branching Brownian Motion (Sandra Kliem and Kumarjit Saha)Markovian Dynamics of Exchangeable Arrays (Jiří Černý and Anton Klimovsky)Contributed Articles:PATRICIA Bridges (Steven N Evans and Anton Wakolbinger)Collision Times of Random Walks and Applications to the Brownian Web (David Coupier, Kumarjit Saha, Anish Sarkar and Viet Chi Tran)A Note on Characterizing Tightness of Random Sets of Càdlàg Paths (Nic Freeman and Sandra Pulau)On Projections of the Supercritical Contact Process: Uniform Mixing and Cutoff Phenomenon (Stein Andreas Bethuelsen)Phase Transition for the Contact Process in a Random Environment on ℤdxℤ+ (Qiang Yao)
Readership: Graduate students, university professors, researchers and professional mathematicians interested in probability theory, and models arising from population genetics. Population Genetics;Genealogy;Interacting Particle Systems;Coalescents;Random Graphs0Key Features:Contains lecture notes and original contributions at the forefront of research in the field of interactive particle systems