The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics. This volume is based on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held January 2–3, 2017 in Atlanta, GA. The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.

Though competition occupies a prominent place in the history of economic thought, among economists today there is still a limited, and sometimes contradictory, understanding of its impact. In Competition and Growth, Philippe Aghion and Rachel Griffith offer the first serious attempt to provide a unified and coherent account of the effect competition policy and deregulated entry has on economic growth. The book takes the form of a dialogue between an applied theorist calling on "Schumpeterian growth" models and a microeconometrician employing new techniques to gauge competition and entry. In each chapter, theoretical models are systematically confronted with empirical data, which either invalidates the models or suggests changes in the modeling strategy. Aghion and Griffith note a fundamental divorce between theorists and empiricists who previously worked on these questions. On one hand, existing models in industrial organization or new growth economics all predict a negative effect of competition on innovation and growth: namely, that competition is bad for growth because it reduces the monopoly rents that reward successful innovators. On the other hand, common wisdom and recent empirical studies point to a positive effect of competition on productivity growth. To reconcile theory and evidence, the authors distinguish between pre- and post-innovation rents, and propose that innovation may be a way to escape competition, an idea that they confront with microeconomic data. The book's detailed analysis should aid scholars and policy makers in understanding how the benefits of tougher competition can be achieved while at the same time mitigating the negative effects competition and imitation may have on some sectors or industries.

Proceedings of the NATO Advanced Study Institute, Cargèse, Corsica, France, 18-31 July, 1988

Non-equilibrium surface growth for competitive growth models in (1+1) dimensions, particularly mixing random deposition (RD) with correlated growth process which occur with probability p are studied. The composite mixtures are found to be in the universality class of the correlated growth process, and a nonuniversal exponent _ is identified in the scaling in p. The only effects of the RD admixture are dilations of the time and height scales which result in a slowdown of the dynamics of building up the correlations. The bulk morphology is taken into account and is reflected in the surface roughening, as well as the scaling behavior. It is found that the continuum equations and scaling laws for RD added, in particular, to Kardar-Parisi-Zhang (KPZ) processes are partly determined from the underlying bulk structures. Nonequilibrium surface growth analysis are also applied to a study of the static and dynamic load balancing for a conservative update algorithm for Parallel Discrete Event Simulations (PDES). This load balancing is governed by the KPZ equation. For uneven load distributions in conservative PDES simulations, the simulated (virtual) time horizon (VTH) per Processing Element (PE) and the simulated time horizon per volume element Nv are used to study the PEs progress in terms of utilization. The width of these time horizons relates to the desynchronization of the system of processors, and is related to the memory requirements of the PEs. The utilization increases when dynamic, rather than static, load balancing is performed.

Jati K. Sengupta examines the market dynamics of the evolution of industry and the impact of new technology with R&D and knowledge capital. The book builds the theory of innovations in the contexts of the high-tech industries of today such as computing and telecommunications.